and it was caused by a fan failure. Once I replaced the fan, it started normally with no additional problems.
Last night my desktop crashed randomly, like there'd been a power failure. I tried to turn it back on several times, each time it would get partially through the booting process before powering down. Once, it made it to a 'system repair' or 'startup repair' process (can't quite remember which), however it commonly makes it to the 'your computer shut down unexpectedly screen' or the Windows icon screen.
I'm running Windows 7, with a nVidia 480 GTX, 4GB of RAM, an i5-2500K. I've had a look on Google for similar situations, and while it seems pretty common, there's not a large deal of information on how to actually go about working out what is wrong.