Suggestions

Less than 2 months ago I bought a 2002 Ford Escape with 165000 miles. It has been nothing but trouble. 3 days after I bought it, it misfired for the first time. It stopped on its own and I let it go because that day the brakes also went out.

It seemed fine for a few weeks and then the check engine light came on it was a code for the 02 censor. Some fuel injector cleaner did the trick.

A week later it started misfiring again. I couldn’t drive it to get the code checked so I replaced the coil pack on the cylinder that misfired last time. I drove it that night it wasn’t misfiring but it would barely get to 50 mph. When I tried to start it again it made a loud squealing when I press the gas. I still don’t have a CEL.

I’d suggest you have several problems, so don’t lump all the symptoms into one problem. First deal with the misfires. Go to a NAPA store and buy a new set of rubber boots. These boots attach between the coil and top of the plug. You can reuse the spring that sits inside the boot. This might solve the misfires without the expense of new coils.

The squeal noise is unrelated to the misfires. An accessories drive belt or serpentine belt is a good place to check.

+1 for @Uncle Turbo, but I’d opt for a new set of plugs at the same time.
If you can release the tentioner’s tention on the belt, you can turn each accessory’s pulley by hand and feel if one may be grinding or feel rough to spin. If all are good I’d just replace the belt.
Whenever you buy a used car with that much age, there are sure to be a few things that are just worn out.

Yosemite

I would have thought that if the belt was the problem it would be noisy all the time and not just when I press the gas. There is a sound in the engine like an air leak but I can’t figure out where it’s coming from.

“but it would barely get to 50 mph.”

Sounds like all the misfires have already severely damaged the catalytic converter

Unless I hear otherwise, I’ll assume when it was misfiring the check engine light was flashing

That means severe misfire, which can damage the catalytic converter. Owners manuals warn you about this condition

it was probably overdue for plugs and boots before you even bought it

The light did flash for about 30 sec both times. I was also thinking it might be the cat. Which is sad. I’m going to get a second opinion but I already ha one mechanic I talked to tell me it would cost 4000.

$4,000? Are you sure you heard him right? Must have been a dealer mechanic.

Attached is a reputable aftermarket source for direct fit replacements. Your shop may have slightly higher prices, but any reputable independently owned and operated shop can replace both converters for thousands less.
http://www.autopartswarehouse.com/shop_years/ford-escape-catalytic-converter-2002.html

Understand that I’m only commenting on the cost you were given to replace the cat converters. It may very well be a clogged converter due to damage from misfires, as db has suggested, and work in addition to replacing the converters may be necessary to correct the cause(s) of the misfires. Or the misfire itself may be the reason you can’t get over 50mph. I can’t tell from here. Clearly, from you other comments, you have other problems to address.

Did it run great when you got it?
How long does it take for a catalytic converter to go from functional to limiting your speed to 50 mph?

Just a round-about comment, but 165,000 miles and 13 years of age are both good reasons to start replacing all sorts of things. Of course, inspect the parts that are needed first in case the precious owner recently did it, but when in doubt, replace it.

A good rule of thumb I use is the “at 10 years old, almost anything rubber needs to be replaced” rule. Belts, hoses, brake lines, some bushings, etc. You can almost bet your paycheck that new plugs & coils will help it run better. I’d imagine that a new fuel filter and air filter would be a good idea. I’m sure the coolant needs replacing too. PCV valve, MAF Sensor clean, etc.

Basically, you have to at least pretend that the previous owner neglected everything.

For the record, dangerous, a cat converter can go from functional to speed-limiting almost instantly. The inside of the cat converter is comprised of a ceramic honeycomb coated with platinum-palladium, an unobtainium in the rhodium family of metals. Misfires can cause structural damage to the ceramic, causing it to crumble and plug the converter up.

I know for sure I heard a hissing noise with the hood up like an air leak but I can’t find it. All the hoses seem fine. I had time to fire it up again. The loud squealing seems to have stopped. I could tell the engine is running rough. I really don’t want to pay to have it towed for a diagnostic. I thought I’m might try taking the 02 censor on the engine side of the converter off to see if it runs better. I’m told this is a way of checking the converter.

The mechanic who told me the price is well recommended here in town. Small shop. He said it has to be custom fitted. I’m definitely going to shop around.

I have to respectfully disagree with @DangerousDIY about replacing everything. This is just throwing parts at it without diagnosing a thing. You could throw $1000 of parts on it only to find that the misfire is caused by burnt valves and the vehicle is not worth fixing.

Why spend $50 to $100 for each coil when you don’t even know if that is the problem.
I’d start with a new set of plugs and when you remove the coils…if the boots look rotted and in bad shape then replace those also.
If, with new plugs it still misses, then have the codes read at an Auto parts store. Most will read the codes for free and give you a print out of the codes. Then post the codes here so we can help. The codes will be in a P0xxx format. A code of P0301 will mean that the #1 cylinder is misfiring…P0305 would be cylinder 5 is misfiring, so at least it will help point you to the particular cylinder that a misfire was detected.

If you feel that there is a air leak that you are hearing…you can find an old piece of garden hose, about 2 feet long. Hold one end to an ear and move the other open end around near the engine and you will hear the hissing get louder when you get close to the spot. Just keep clear of any pulleys and the belts when doing this and pin your hair back.
We don’t want you to be changing your screen name to BaldspotShandra!!!

A belt can squeal all the time or only at idle, sometimes only at acceleration.

I would relieve the tentioner while spinning each pulley and feel for any roughness. You will not be able to turn the crankshaft pulley, so don’t be alarmed when you can’t. All the other pulleys should turn freely, though some will be easier to spin than others.

Also if it squeals at start up…to test if that is where the problem is…spray a little water onto the belt. If the squeal goes away it’s the belt or a pulley. But it will only remove the sound until the belt dries out in a minute or so.
You should also look for loose covers and shrouds that may be rubbing on the belt or a pulley.

Yosemite

My feeling is that there are multiple problems so the first thing I’d want to do is run a compression test. The spark plugs are first up for a look and while they’re out run the compression test and determine from the get-go whether or not mechanical issues exist.

If there are issues then parts replacing can be an exercise in futility. Hopefully the compression is at least reasonably tolerable.

There are some other points to be made but if the vehicle were mine I’d want to know what I was dealing with mechanically before heading to the parts house.
Maybe the seller knows more about this vehicle than they let on…

+1 for @Ok4450, a compression test would at least show you if the engine is worth saving.

Yosemite