Few things it could be, but quite often when your computer powers off after a task that requires some extra loading it means your power supply is too low wattage, if you simply pull the side off ur case and look at the power supply and see how many watts it actually is, if it is about 250 or lower, you need a new one and that is probably why. If it is around 300 then it could still be your psu, but higher than 400 I doubt it will be unless you have an x850, 512 ram, athlon xp 3200 sorta spec.
Yes, the wattage you need depends generally depends on your CPU and your drives (CD/DVD/Hard). You should check your hardware manuals for more information.