pc shut down on its own.will not start up?

Remove power, then open the case and look inside. Is it dirty (lots of dust and stuff)? If so you probably have heat damage, but try cleaning it out thoroughly with a can of compressed air and a soft brush. Of special importance is the fan for the power supply and it's internals (blow this out well), the fan and cooling device on the CPU and the fan (if there is one) on the video card.

If that doesn't help then I would suspect your power supply has died.

Before replacing it, remove everything from the computer except the mouse, keyboard and display. That means removing all PCI/PCI-E cards and all USB devices.

Also remove all memory. The computer won't work that way but it should at least power up and beep at you.

If still no good, then almost surely the power supply is gone, though there is always the possibility that capacitors on the system board or have gone bad. This link has some good pictures of what they may look like: Capacitor plague - Wikipedia, the free encyclopedia