I'm 96% sure that your problem is with...
the main relay located up under the dash just caddy-corner to the steering column.
My car had the same problems:
Would start sometimes. Other times wouldn't
I'd cut the car off, run in the store for a coke, come back out, and it wouldn't start. I'd have to sit for about 5 min. or so before it would start again.
After about 100-150k miles that damn relay just goes in and out.
Replace it and you should be in business.