Please, help me solve the Mystery of the insane start-up procedure!
Normal procedure for this car:
Try 1: hop in car depress clutch, and turn key. Results in the starter whining, and rarely starts the car.
NOTE: multiple attempts at turning the key only results in whining.
Try 2: shift through all 5 gears & reverse, and after each shift I will attempt to start the car (turn the key).
Result: after a couple times through the gears the starter will “chose its favorite gear,” begin to turn, and then the car magically comes to life. The “favorite gear” changes on each start (3rd, 1st, 5th, R, 2nd. 4th , etc. etc.).
Extra Toppings: The car may also start based on if the drivers door is left open (while the gears are being shifted through), or if the door is shut.
INFO:
This car is one of my parents old cars. I used it for a high-millage Summer job 2-years-in-a-row ('06 & '07) in which time this problem only appeared at the end of those 2 Summers.
The car also had an overheating problem while I was using it. To keep the engine from going in flames I would have to turn the vents all the way up high. This was with temps above 100F, so the inside of the car was, I’m guessing, around 150F 
Sounds like a loose, or bad neutral safety switch. I highly doubt any door opening combination or anything else like that really has anything to do with the car starting or not. Does it make a difference how you hold your tongue, or if you make a certain face? J.k. Check out the NSW. You might find it loose.
I have an alternate guess. It sounds like there is a problem either with the starter’s gear engagement or with the flywheel gear of the engine. Running through the gears may move the flywheel ever so slightly as to allow it to start. I don’t think the starter would “wine” if it were the neutral safety switch. I also think that the driver’s door being open is unrelated.
I agree with tardis. I think if the starter is making any sound other than “click”, you can rule out neutral safety switch. My money’s on bad starter bendix or a bad flywheel. While I think tardis may have something with the idea that shifting through gears moves the flywheel a little, I think that it really has very little to do with solving the problem.
TRY THIS: Next time that it won’t start, put the shifter in 1st gear, hold the clutch, open the door, then push the car backward or forward a couple of inches with your foot (obviously you will want to do this on level ground.)
I’d bet that it starts right away, and that means that it’s a flywheel problem.
So in conclusion, it’s got to either be the starter or the gear teeth on the flywheel. A mechanic will be able to remove the starter, test its bendix drive (the mechanism that causes the starter drive gear to mesh with the transmission and then retract when you release the key) and inspect the flywheel gear teeth. The flywheel repair is going to be a few hundred dollars (probably 500+), the starter should be considerably less. So hope for bad starter.
Just sounds like a starter issue, time for another one. The electric motor part of the starter seems to be working just fine ( the whining sound is the armature spinning in the starter ). It’s either; not kicking out the drive to meet the flywheel, bad ratchet mechanism in the drive, or teeth bad on the flywheel or drive. I think it’s not kicking out the starter drive and the actions you mention doing, create enough vibration after a while ( finaly equivilant to tapping on the starter) to free the mechanism inside the starter. Just go to the parts store and get a reman and be sure to have a look-see at the flywheel teeth by manually spinning the crankshaft a full revolution.
I agree with the posts who suspect that the flywheel ring gear is needing some new teeth.
When you twist the key to “start”, the starter solenoid becomes energized. That moves a lever that slides the starter gear into engagement with a ring gear around the outside edge of the flywheel, and also connects some contacts that complete the starter motor circuit.
I think you’re hearing the starter motor spin without its gear engaging the ring gear…likely because of missing ring gear teeth. If the solenoid itself were not working and the lever levering (levering?), then the starter motor circuit would not be completed and all you’d hear is a click. Or perhaps nothing.
If the neutral safety switch were operating intermittantly you’d hear nothing. No activity would happen in those tries where the engine didn’t turn over.
Missing teeth can cause this intermittant starting condition. Repeated trys can “jar” the flywheel enough for a tooth to catch.
Thanks for the replies.
I Thought the problem might be in the clutch, but I’m still (ignorantly) hoping its not.
I’ll try what mr josh suggested first.
I’ve never manually turned a crankshaft before. Is there anything I need to know/remove first? Is the flywheel ring gear clearly visible, or just the main flywheel? Thanks.