Gyrene, I've suggested looking for swollen caps first on the motherboard, then on the PSU. Oh, and BTW there's caps on the graphics card, too.
As you suppose, freezing often is a symptom of overheating but IMO that doesn't explain the loss of passwords. Overheating just slows the computer down to a lock up.
And a bad cap is always a bad cap. Inside a PSU caps among other components produce 5 and 12 volts DC from 240 volt AC. On the motherboard there are several current regulating circuits to make 1,65 or 3,3 volts etc. I'm not a trained electrician, but I've worked with malfunctioning computers for the last seven years and the strangest symptoms have most often been due to a failing mobo or PSU.
Yet another hint, now that overheating has been mentioned: Look for dust between fans and fins.