I assume that this is a desktop PC and not a laptop. (if it's a laptop - take it in for repair - there is nothing you can do)
Trace the video cable back to the PC. The cable can be plugged into two things:
1. a socket on the motherboard near where the keyboard and mouse sockets are
2. a socket on a video card this is in turn plugged into the motherboard (removed from the area of the other sockets).
If you have the second configuration you can remove the case cover - remove the monitor cable - remove the screw holding the video card - remove the video card - dust it off - replace card - reverse the steps and reassemble the PC.
Restart the PC.
If this doesn't work then it's time to take the PC to a repair shop.