97 Rav4 Intermittent Start Problem After Short Drives

I have a 1997 Toyota Rav4. 2nd owner. No accidents. Regularly maintained at a mechanic. No issues until this one. I searched the forums looking for an answer, seen similar but not exactly my issue. The car has an intermittent starting problem. This never happens in the morning. It only happens when the car is driven a short distance. When the key is turned to start the car, the engine does not crank. All the electrical comes on. We had the starter rebuilt. I have had it towed to my mechanic five times. Each time, when it is unloaded from the tow truck, it starts right up. We have left it there overnight and all day. They cannot replicate the problem. I drove the car to a friend’s house 1 mile from mine and it would not start for 24 hours so I had it towed to the mechanic. Again once it was unloaded it started right up. A couple months ago we did a major service with a timing chain/belt. It did not happen for a couple months. Now twice in a week it has happened. My mechanic will not do anything more until it fails completely.

Could be the ignition switch. When it doesn’t start, try wiggling the key.
Could be the battery cables, either the connections or the cables themselves. Have the cables removed and and the connections cleaned and the cable itself checked.
Could be the starter relay, usually part of the starter.

Some simple checks with a voltmeter when it won’t start should narrow down the possibilities. Perhaps you could borrow one and have the mechanic walk you through a check, showing you the points to attach the meter.

We had a similar issue on a ford, towed to the dealership twice under warranty where it started right up. it seemed after it sat about an hour it would start back up. Talked to the dealer and they were willing to look at it right away if it failed so I had my wife stop there every time she passed by. After a few tries got the no start at the dealer, they figured out it was the fuel pump. There are so many options diagnosing it in failure mode is the best way to fix it.