Could be a bad PSU? even if you've tried 2, weirder things have happend. Loose wires maybe? Also sounds daft, but make sure all the case fans are spinning, if not certain components will overheat, as you probably know. Some cases have more fans than others, so I'd pop the side off the case while the machine is running ( I know they tell you not to do this, but it's ok so long as you don't touch anything, I've seen it done many times). Also give it a quick squirt round with some compressed air while it's turned off, place a pen in the fans to stop them spinning & spray them too. Clean the fan filters & check over the other components for dust bunnies.
Where are you sitting the case unit? Make sure there's at least 6 inches each side for the fans to pull air in.
Also this will probably sound stupid to you, your obviously an expert, but I'd double check the power saving settings, make sure it's not going into sleep mode. I had a problem a while ago on my computer that allowed it to go into standby, but each time it did, it shut the system down as turning it off would. This got fixed when I had it repaired back in feb for conficker.
It also sounds like a symptom of some worms, because a while ago, when blaster was the latest threat, mum got it on our computer, which made it shutdown over & over. Get it into safe mode, run virus & spyware scans.
Also have you tried running it in safe mode? I'd leave it in safe mode (no networking), with minimal stuff running for a while to see if still turns it's self off. This way you can find out if it's the OS or hardware, because if it's hardware, it will still do it, albeit later than before because less data is being processed. Just a thought.
I'm not experienced with ME, but I assume it uses simlar principles to other windows OS.
By the way, I want to steal your job It's something I've always wanted to do.