I know, this answer is probably too late for you, Justin, but I had the same problem for quite a long while with 1987 celica GT. The car would drive somewhere with no problem but, ten minutes later, it would not start. No crank, nothing at all. The car was dead. I changed the battery several times and it would get better but soon it would recur. I changed the starter with no effect. I was about to change the neutral safety switch when a smart mechanic spotted the problem. The car doors sagged ever so slightly over the years and would spontaneously lose contact with the "door closed" system. In effect, the doors would register as "open" and kept draining power intermittently. The guy fixed the doors and the problem disappeared. God bless him. This is 15 years later and the car still drives fine. There was a problem with fuel pump for a short while also but that is another story. I hope this helps at least some of my fellow Celica enthusiasts.