When my power supply went bad a few months ago, it would just cut off all of a sudden and I had to wait until it cooled back down to get it to boot up again. It never randomly restarted. When I was trying to figure out the problem, I took a floor fan and placed it right next to the case and it worked fine. That's how I knew it was overheating. I don't know if this helps you any, but I hope it does. Maybe there's a loose connection in there, like the connection to the reset or power button. I don't know if this would randomly restart or do something else, but it's worth a look if you haven't tried already. Hope this helps.