I would also initially guess a software or power/contact issue, but it sounds like you've triple-checked all the basics. How about reducing the RAM on the BPPC to one stick, or trying a single different one? You might also end up trying another motherboard, or thoroughly checking yours for failing capacitors.
I had a similar problem once with a Picasso IV on an A2000, that had previously worked fine. Random garbage, that eventually progressed to lock-ups. After trying a million different things (and suspecting a dud PIV), it turned out to be something defective on the motherboard.
