Why would 94 Camry not start or turn over if driven for less than 10 minutes for the first time during the day and then start after couple of hours Would a car alarm have anything to do with it?

Hi, I have had the same problem in two Camry's, it is a faulty/worn ignition switch an easy way to over come this is to fit a cheap relay into the starter circuit external to the starter, this will fix it.