That's a good suggestion. Also, what about an intermittent short on the power button?

Is the PC actually fully shut down or did it get placed into standby mode? Did it shut down gracefully or did it just lose power?

Some operating systems have an option as to how to behave when the power button is pressed. See if the power button is programmed to "Shut Down" or to "Standby". If the former, set it to the latter, and observe the behavior if you leave it running overnight.