Short of being totaled in an accident it is hard to picture a car any more dead than a car with a bad engine and blown transmission.
I would get into the habit of checking it at least every 2 weeks.
I, along with a very large majority of the posters here, do not recommend using these quick lube in and out type of places. Use a well recommended local independent mechanic. They’re also not measuring your oil as it comes out.
My guess (and it’s a guess) is that the previous owner really abused the hell out of your Corolla…ran it hard, chronically let the oil run low, extended oil change time, etc. The engine was close to worn out when you got your hands on it. One thing you’ll see on pretty much every “which used car should I buy” thread that starts on here is that everyone recommends taking a potential used car to your local independent mechanic and paying them 100-150 to do a thorough inspection before you purchase it. Will they catch everything? No, of course not, but they greatly increase your odds when you’re purchasing a new vehicle. And keep in mind, too, not every Toyota will be the picture of reliability, sometimes they just aren’t. And on the other end, I’m sure we’ll eventually find out that someone got a Nissan CVT past 200,000 miles without an overhaul or replacement 
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The mystery is likely in these first 34K miles.
It might be a leased vehicle.
It is not unheard of what people leasing vehicles do not do ANY maintenance, including overextending the change intervals and sometimes even completely skipping on oil changes.
You just do not know when you get one if it was properly maintained or if it was “flushed” from tar-black oil shortly before the sale.
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As others have said, you need to stop doing that. I wouldn’t trust those guys with washing my car, much less messing with the engine. There are plenty of horror stories from honest quick-change places because they hire incompetents who work cheap,and not all of them are honest. Some will charge you for services they never perform, for instance. For all you know you went 30,000 miles between actual oil changes.
At any rate, that car was likely neglected. Either by you / Valvoline, or by whoever had it before you. The most reliable car in the world turns into a hunk of garbage if it’s not maintained properly.
I concur with the others- junk it and get something else, and take the new one to a local, independent mechanic for oil changes, not the fast-buck places.
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+1
Absolutely on target.
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Additionally, most of those places use cheapo “white box” (no brand name whatsoever) filters from China. That is one more way to damage one’s engine, IMHO.
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This all may be true, and would certainly explain the engine developing bearing problems at a young age/low mileage. However, this does not explain the alleged transmission problem, which I am seriously questioning anyways. No car requires any maintenance to the transmission during the first 36,000 miles, and no lack of maintenance would cause the transmission to break apart inside and crack the case, which is what the mechanic seems to think happened.
Before junking, selling, or disposing of the car, I would get a second opinion from another shop. Also, I still have not seen an answer to the question, does the engine still start and run? If not, why is a transmission problem even suspected?
There is a problem for owners who don’t check their oil. It is called extended oil change intervals. When oil was changed every 3000 miles, most cars did not burn or leak enough oil to run low between changes and cars that did burn oil warned their owners by smoking.
Now the oil change interval has been changed to 10, 000 miles or I year for your Toyota. the catalytic converter burns up any oil going out the exhaust and the oil is much thinner than the old days. 0W20.
I car does not have to burn a lot of oil to completely run out of oil in 7 to 10 thousand miles. Your owners manual suggests checking your oil once a month. I suggest doing it on the first because that is easy to remember.
It is too late to save this car, but you don’t want to lose another engine, do you?
A Triple AAA certification means nothing. My youngest son lives in a neighboring city about 70 miles away. He took his Lincoln Aviator into this facility some years ago for an oil change. They recommended a fuel filter change which was quite likely needed. He paid and left.
A few weeks later while visiting I decided to check and found the original fuel filter still in place.
As for relying on a fast lube tech to tell you how much oil was in the engine that is something that should be taken with a grain of salt. They pull the car in and the guy underneath removes the drain plug and lets it out. We’re supposed to believe that his opinion of oil draining is accurate? And quite likely he never watched it and flat does not care anyway. That is just someone BSing in the moment.
If you or your husband do not develop the habit of checking fluid levels on a regular basis you WILL be repeating this scenario again on another car.
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Things happen. The OP has two other older vehicles that apparently haven’t.had problems. With the age of the Honda, it might use a little oil. If so, unless I see evidence to the contrary, I would believe they monitor the oil level. The Corolla seemed to be o.k. for the first years the OP owned the car. I do wonder when the engine knock first appeared if something could have been done.
Many years ago, our family car was s 1949 Dodge. The car did use a little oil, but my dad was very careful to check the oil at every fuel stop. He had filled the gas tank and checked the oil just before we started out on a 300 mile trip. About 225 miles into the trip I noticed the oil pressure gauge fluctuating all over the scale. I was in 6th grade at the time and my dad had explained to me what the gauges meant. I brought it to Dad’ attention. He immediately pulled off the road and checked the oil. No oil showed on the dipstick. We walked to a gas station and bought 2 quarts of oil. That brought the level to the add oil mark. We then drove to the station and added another quart. I had been getting 50¢ a week allowance for doing chores around the house. I got an extra 25¢ for saving the engine.
My dad did a lot of business with a DeSoto/Plymouth dealer. The head mechanic was also the service manager. This service manager would often tell me about a car that had a difficult problem to diagnose and that he had solved and then he would question me about what I thought he had to do to fix the car. One time when I went in to pick up our family car, he took me over to see a 1957 Plymouth V-8. They had pulled the engine and the crankshaft had broken. He asked me what I thought had caused the crankshaft to break. He didn’t agree with any of my guesses. I had thought that the oil had gotten low. “No”, he replied. " The crankcase was full when it came in and the oil had been changed". After I made a couple other guesses that he said couldn’t be the cause, I asked him what had caused the crankshaft to break. His answer was “Things happen”.
At this point I would suggest this same answer to the OP. “Things happen”.
If it needs a new engine and trans I say bail.
In that case, I wouldn’t be surprised if you return here in the future with another dead engine. Engines can and do start losing oil for various reasons. Are you really willing to gamble with another few thousand dollars?
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Regarding Triedaq’s comment about a broken crankshaft I might add this. More than a few times I’ve seen cars come in with a seized engine, thrown rods, holes in the block, etc, etc and in most cases they were full of motor oil. Fresh motor oil with a new filter. I suspect that 57 Plymouth also had fresh oil in it.
Some people seem to think that fresh oil and a new filter will be the answer to a non-repairable engine problem OR they are trying to cover their negligence tracks. One of them was a VW with a transverse mounted 4 cylinder which had a fist sized hole in the front of the engine block and 2 connecting rods sticking through it. Again, full of fresh oil/new filter and a “Why no, I check the oil level every week and it has never been run out of oil” excuse.
This was a car with 12k miles on it and which was towed to the dealer around 11 at night and dropped off with an Early Bird ticket. He tried to blame us but under some grilling he admitted that the hood had never come up in the last 9k miles.
Regarding the decision, you have a 7 year old car with the two most expensive assemblies in it needing replacement. Break out the big fork, it’s done…
How do you know the filters are from China? They’re in a white box with no identification. China is certainly on the short list, but cheap filters could be from anywhere. When I have car maintenance, all manufacturers are identified on the parts list, just as you do.
@TwinTurbo. I missed that piece of evidence. I grew up where we had to maintain our equipment. Back before self service gas stations, most attendants did check the oil. We also knew how to pull the dipstick and check the oil.
Us regulars on this board have a knowledge of and respect for machinery. I have never had to add oil to any of my recent cars. Even my 1978 Oldsmobile Cutlass with 240,000 miles never used any oil between changes.
Another vote for simple oil level monitors and oil pressure shut off switches. They really are very cheap to provide. My Rivs had both and although never used oil between changes, the use of a quart a week all of a sudden due to a pan gasket leak quickly provided a warning message. You can be surprised when things go wrong unexpectedly and these are very simple solutions. Just a couple switches and some wires.
The latter 
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Thank you all for your insightful comments! I’ve learned a lot from everyone here. It never occurred to me, simply because I haven’t had major issues with any car before, to check my oil levels myself once a month, or that valvoline wouldn’t be the best place for maintenance and oil changes. I am definitely going to start checking my own oil on the first of every month as someone suggested, and also find a local mechanic that I can trust for oil changes and other work.
I am almost positive that the car, before we bought it, was either a leased vehicle or one rented out by a place like enterprise. I seem to recall something like that coming up either in conversation with the dealer or in the vehicle history (which I no longer have). I also recognize it’s highly unusual for a Toyota to fail like this so something pretty significant must have happened. The second option it seems is that there was an issue with the cars oil and that valvoline never said anything, even though we always got our oil changed well before being on schedule, and that this messed up the engine permanently. To be honest, I didn’t even notice the engine knock when it first appeared. My father rode in the car and noticed a very light, subtle knocking that he pointed out to me.
To give an update on the car situation. We had the car towed from the audio repair shop back to our street where a mechanic friend lives. He put it up on jacks and said the transmission seemed fine but there was something with the washer that needed to be fixed. The part was only $15 or so plus labor, which is deeply discounted bc he’s a long time friend. The car does turn on, but the engine is definitely dying (he is now third to confirm
This) and he said he could replace it with a used one for $1600 plus labor, around $2200 total including the transmission work. My husband wants to do this because he trusts his friend and because he doesn’t want to risk spending $2000 on a much older used car, so he’s going ahead with it as he needs it for work.
I’m really grateful for everyone sharing your knowledge here, and also for being kind and not snarky at all due to my own lack of knowledge.
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You could easily loose that much money on any used car purchase, good luck!