PSU is a prime candidate then, are you positive you have all the power connectors plugged in? I have seen motherboards with as many as 4 different power connectors.
Thing is, I've had this computer up and running fine for several months. It was just recently that this started to happen
Maybe a connector got unplugged while somone was cleaning it? But then again, the computer works fine most of the time (I'm not it right now with no issues) and seems to turn off at weird times, such as when playing games (but not always). Maybe we'll find the answer in the voltage readings I've posted above?