2002 Saturn SC2 Randomly Doesn't Start

I have a 2002 Saturn SC2 that has, over the last few months, randomly been failing to start. There has not been a detectable pattern, except it seems to happen only after the car has been running for a while - while out doing errands, for example, not when starting it for the first time of the day.

When this happens, the lights/electric come on, but the engine doesn’t turn. Sometimes it makes a clicking sound, like it’s trying to do something. If left alone for a while, maybe 30-60 minutes, it usually will start.

I’ve tried all kinds of tricks, locking and unlocking doors, putting it in reverse and neutral and trying to push the car, jiggling the steering wheel, pumping the gas, etc etc and nothing seems to work when it decides to quit.

I’ve taken it to two different mechanics, and neither could figure out what was wrong with it. The car started every time for both of them.

I’m wondering if it could be a computer code or a bad connection in the ignition somewhere. This car has stumped two mechanics on opposite ends of town … I would greatly welcome any ideas as I had to miss work this week when my car randomly decided not to start!

Thanks very much!