Also, if the pc turns on for a few seconds but then turns off, In my experience it may be a CPU overheating issue. However if it stays on and you have to turn it off, it could be the graphics card, (If you have one that is) it could be the video out on the motherboard, it could be the monitor, or it could be something as simple as the display cable.
To test if it is the graphics card plug the display cable into the motherboard and try to boot it up, if you get a display you need a new graphics card.
To test if its the motherboard you can get a different cable and plug it into a different spot on the mobo.
To test if it's the monitor and you don't have another monitor you can plug it into a T.V.
Cable is self explanatory.