Sporadic Starting Trouble

My car is a '96 Pontiac Grand Prix SE with 188,000 miles. I know my description of the problem will more then likely do nothing but raise questions so I’ll give what info I can to help.

First the problem: As the title states it comes and goes with seemingly no connectable circumstances. Sometimes it doesn’t happen for months other times it can happen 2+ times a week. When I try to start my car there is no sound at all from my engine/starter/alternator. But here’s the kicker all I have to do is wait 5-15 minutes and it starts fine with no trouble.

As for what I’ve had done: I’ve had several shops look at it and all have come up with nothing for an answer. I’ve had wiring changed, spark plugs replaced and all the shops said my alternator and starter were fine.

I wish I could give more information but I don’t know next to anything about cars (though I do want to learn).

When this happens do all of the dash lights come on?

The next time this happens, put the car in neutral and then try starting it. If that works, just report it to your mechanic and s/he will check out your neutral safety switch.

Apologies, I knew I forgot to mention something. Yes all the electronics turn on and work just fine. I’ll keep the neutral starting tip in mind. Thanks!