'91 Prizm won't turn over

This is a problem I've been trying to diagnose for a while now.

The car starts fine when cold, but occasionally will not start after it has been run for a while and parked for a few minutes. The starter refuses to turn over, and acts as if it is not getting any current at all.

After the car has cooled for a while, it starts fine and runs with no problem.

The weather conditions don't seem to have much to do, other than it's usually a warm day when it happens. It seems to happen more when the morning is cold and the afternoon is warm.

I've replaced the starter, battery, positive terminal and the entire negative cable assembly and most of the ignition system with no luck. Anyone run across this before, and what was the fix?

Thanks!

check the ignition switch behind where you put the key in the dash, mine fell off but they can just loosen and could be coincodental that it does it when cold.