What was the ambiant temp in the room the day this happened?
Is you PC's internal speaker plugged in?
Are warnings enabled in your BIOS?
Is your monitor powered directly from the wall or from the PC's PSU? Try powering it from the PC's PSU and next time the fault occurs check if there is still anypower going to the monitor(is the monitor's stand-by light lit).
Does the Fan in the PSU work, and was it still going when the PC lost power?
If you've got a couple of spare dollars i'd suggest buying a new PSU as they are relitivly cheap and could fix the problem.. or at least tell you what isn't causing it