To any computer hardware minded people on my list, please check out all the details on this forum post at GameHavoc. It lists all the parts (with links) that have gone into it and everything that has happened. You don't have to reply there, though.
Does anyone have any clue what's going on or what I could try doing or replacing next? At this point I'm thinking a new CPU and possibly yet another motherboard are in order. I'm half tempted to see if I can get a manufacturer replacement of the parts, although I have to act soon or it will be past the 1 year replacement warranty on several of the original parts.