Sounds like something's overheating, and it it's not the CPU, it's something else that should be heatsinked but isn't. Tried touching all the chips and heatsinks? You're looking for a chip that's incredibly hot, or a heatsink that's cold (because it's not sinking heat). I don't know if you've done it already, but in the minutes available to you before it locks up, I'd nip along to the "turbo settings" or similar, and set it to safe, or default mode or whatever it's called.
But what I'd personally do about now is sneakily buy another motherboard without telling anyone.