Sounds very like a duff M/Board to me.
I spent a lot of money on a high spec build about 8 years ago & it suffered from completely random issues like you describe, unrequested hot boots being the biggest problem, The OS was fresh installed several times, the memory, graphics, power supply & HDD's were all swapped out, but the problem persisted.
After much urinating about the board was replaced by the manufacturer & the problem was sorted - turned out to be a faulty batch of Intel ICH's that were fitted with their new "killer" chipset of the time - cant remember which, but It will pre-date your M/B.