Is it the monitor or the PC? The easiest way to know for sure what works and what doesn't is to connect a working monitor to your PC. If the test monitor works, your monitor is bad. Alternatively, you could connect your monitor to another PC; if it works, something in your PC is bad.
If your monitor is defunct, you may find someone who can repair it, but usually a replacement is in order. You might even take it as a reasonable excuse to upgrade to a larger or better model.
If the problem is in your PC, listen carefully to your system as it powers up, and look for a green power-on light on the front of your PC's case. If you don't hear the whir of your hard disk spinning up and the hum of your power supply fan--which should be visible on the rear of your PC--then you're not getting power to the PC. The likely cause: a bad power supply that will need replacement.
If you suspect the power supply is bad and you're comfortable with playing inside the case, replace it. But before you do, try re-seating your PC's expansion cards: Sometimes the cards can partially work their way out of their slots on the motherboard.
Avoid touching the faces or chips. Make sure all the power connectors for your drives are firmly seated as well. Then try powering up again.
CRT (Cathrode Ray Tube)
LCD (Liquid Crystal Display)
HPA (High-performance addressing)