The problem is with your video card.
If you have on-board video (the monitor is plugged into your motherboard through the back of the computer) and a PCI or AGP video card attached to the system, the computer will default video output to the PCI or AGP card, so if this is the case, ensure that the monitor is hooked up to the video card.
If you have a video card, and the monitor is hooked up to the video card and you still get no signal, remove the video card and reseat it. (Preferably in a different PCI or AGP slot if possible).
If after this process you get no signal, or you have only on-board video and get no signal, your video card is damaged, and you will need to purchase a new one.