Hopefully, it's the same old boring solution
Those boards (I still have two of them) and a couple of their predecessors were notorious for having capacitors, particularly the ones near the processor slot, go bad. Take a real close look at the green can-type thingies near the slot and the 3 or 4 larger ones slightly further away, toward the backplane.
If any of them have bulging tops (they should be completely flat), are split on the sides or appear to be separated at the bottom, there's your problem. The boards can be recapped by any good TV or electronics technician, but your average computer bench tech won't have the desoldering equipment necessary. My local shop has a guy who works on monitors and such and he has the tools and experience necessary. Usually runs me about $45
One of mine had had a partial cap job already, and now a half-dozen of the little ones right by the slot let go. It was doing the exact same thing. Sigh... back to the shop....
OH! one other thing, pull the northbridge heat sink (the green one) and see if there's any thermal goop under there, bet ya there isn't. That can cause all kinds of goofiness and "acting like it's posessed" behavior. If a cap job doesn't help, look into the power supply, it may be giving up the ghost, but those motherboard caps would be the first culprit I'd check for.