Some more information would be certainly helpful here:
- Do you hear a beep at all?
- Do you see anything on the screen at all? Or is it completely blank?
I would suggest you to check the RAM modules to ensure that they are seated properly. If you know how to, you should remove the RAM modules from your motherboard and then re-seat them to confirm that they fit in place, properly.
You could also try cleaning your PC's motherboard and components, while paying the most attention to cleaning your computer's heatsink. Be careful while handling the processor as if you bend any pin on the motherboard's CPU socket, or damage the processor in any way, things will get ugly.
Also, in some cases, I have noticed that lack of SUFFICIENT power can also cause the computer to sometimes shut down prematurely. So the question to ask yourself, is, have you recently added any hardware component to your PC?
When you turn on the PC, do you see your power supply unit (PSU)'s cooling fan starting to turn? Or is it not moving at all?
Please provide as much as detailed information as you can, since that would help us understand your problem much better.