2002 Saturn L300 engine sometimes won't turn over

I have a 2002 Saturn L300 V-6 3.0L. The car always starts okay when it’s cold, like overnight cold. After I’ve run it for at least 20 minutes to half an hour, then turn it off and leave it for about the same amount of time (i.e., 20 minutes to half an hour), it will sometimes, but not always, fail to turn over when I try to restart it. The battery is fine, there’s plenty of juice, the starter cranks aggressively, but the engine won’t fire up. My mechanic said the fuel pressure was low, about 20 lbs, when it should have been 50-70 lbs, so he replaced the fuel pump, but the problem is still there. He also blew air through the fuel lines to test for obstructions, but there were none. Now he thinks it could be the on-board computer or a defective anti-theft device which is intermittently sending the wrong signal to the fuel pump. On one occasion when the car wouldn’t turn over, he said there was 0 lb fuel pressure. Since the car starts maybe 90% of the time with no problem, it’s difficult for my mechanic to work on it. He doesn’t have time to drive it around town to warm it up, and I’m getting tired of going to his shop and taking the car out for a spin once or twice a day in the hope that, when I bring it back to him and we let it cool down, it won’t start. Anyone have any ideas what else to check?

The problem might be with the fuel pump relay. This relay is located in the underhood relay/fuse box. So if you park the vehicle and the engine is hot, the heat might be effecting the relay where it doesn’t turn on the fuel pump when attempting to restart the engine.

Tester

Cranking and turning over are the same thing, Turning over and firing up or running are not the same thing.