I'd guess at the CPU. It's more likely because the both Prime95 and the Burn test are aimed at memory/CPU issues.
If you get a new CPU, purchase it from a place that'll let you return it if it's not needed (just in case).
As you probably remember, there were a lot of other issues that we initially through were motherboard problems. Also, power supply problems can cause low level system problems, as can memory located in places other than the CPU or RAM (such as Video RAM).
What I'm saying here is that we're playing a guessing game at this point. If you guess right, things are fixed - if you guess wrong, we'll have to check more stuff (and this is done by replacing parts, so it can get expensive).