Sure enough, it died again today.
Tried disabling hyperthreading again and, just like before, it started shutting down immediately, rather than waiting until it actually started to boot. I'm beginning to think it's the motherboard--Rev 1.6 if I didn't say before--or perhaps incompatible RAM. None of my checks complained about the RAM though, but they're Corsair Vengeance DDR3, 4 4GB sticks, 1600MHz v. 5.12. Not sure if that helps or not.
Any more ideas?
Cheers,
Matt