Are the lights coming on at all? If not, my first guess would be the power supply. A failing power supply will reset your computer. There are a myriad of other issues it could be (motherboard for one), but that is the easist to test out.
If you are fairly knowlegable, find a computer that is similar to yours and see if you can swap the power supply. Just be very careful to put all the right cables back, and don't force them into place.
Good luck!