I was driving my friends 91 Lumina with a 3.1 and automatic for as long trip. About 2 hours. I get there and she ran great the entire trip. I shut the car off and then try to start it about 5 minutes later. It cranked good just never fired off. I tried keying it off and keying it back up about 5 times and absolutely nothing happened. It cranked but there was definately nothing happening. I didnt have any tools so i could check for spark or anything. But after the car sat for about 20 minutes it fired right off and ran like a top.
I am thinking that engine was "lost" you know couldnt read where it was in the crank revolution. Any ideas would be great.

 

the most common problem on that car matching your description would be a problem with the ignition module.