The symptoms are consistent with the thermal protection shutting the processor down.... I woud check the processor cooler; check the fan visually if it works, check the contact between processor and heatsink and if necessary refresh the thermal grease. Rectify any overheating causes, and see if the computer will stay on. Also check the Power Supply cooler fan.
If the problem persists you'll have to make the information a bit more specific... like; Do you see anything on the screen,.. the Motherboard logo or BIOS post?.. does the Windows loading screen stop or does it show at all?... How long the wait before trying again?