Computer keeps turning it's self off?

Hey people, our computer keeps turning it's self off randomly, and it could be anywhere from about 30 seconds to about a good half an hour, after turning it on. We would do a system restore or a disc clean up thingy, but the computer its' self wont actually stay on for anywhere near as long as we would need it to.

Any advice people?!?! this is driving us absolutely crazy!