Clean it first. - Then make sure all your fans are spinning.
Heat causes all kinds of wacky problems with electronics.
If after a good cleaning she keeps shutting down, then you can figure out what's causing your problem.
At least then, if it is the power supply, or motherboard, you wont get a face full of dust replacing them.
My old box was so dirty that when the power supply intake fan died, i couldn't tell from looking at it.