My first idea from what I saw you post from this morning is get your hard drive out of the machine ASAP so stray currents don't fry that - you can always slave it into another machine to get your data later. After that, the other ideas are pretty good. Strip it down to the bare essentials (MB, power supply, minimum ram, CPU - that should be about it) and boot to a live drive (I suggest Hiren's boot CD - it is pretty good with lots of diagnostic tools, though nothing so easy as "run" -> "here is your problem..." solutions). If all the flakiness continues (I think you already did close to this and said it did), change the Power Supply (if possible). Once that is changed, if it still continues, swap ram (again, if possible). If it STILL continues, replace the MB/CPU assembly. The price difference (timewise) in general for finding the individual bad component and replacing either the CPU or Motherboard is not worth it compared to the cost difference of replacing both.
I think you are about 30% there already, so if you do continue to work on it yourself, that would be how I would do it. You don't need to find the problem, just isolate it and replace. BTW: If it is the MB/CPU, make sure you pay close attention to your PSU and backup plan religiously. It might well be a flaky PSU caused the MB/CPU to go bad....If it isn't too hard financially, it might be worth replacing the PSU anyway and keeping that one as a spare if it seems good.