Check the obvious. Start by checking all your cables--monitor, keyboard, and others--as well as the power cords for both the computer and the monitor. It's best to completely unseat them and re-attach them to ensure you have a solid connection; a connector that looks and even feels like it's firmly attached may not be. And don't forget to check the power outlet and your surge protector. Some surge protectors come with fuses or circuit breakers that can be triggered by an intermittent power surge. Usually a surge protector has a small button that you can press to reset it and get the power flowing again. You might even try an alternative power cord to make sure that hasn't gone bad.

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.

Reference

Display monitors must be refreshed many times per second. The refresh rate for a monitor is measured in hertz (Hz) and is also called the vertical frequency, vertical scan rate, frame rate or vertical refresh rate. The old standard for monitor refresh rates was 60Hz, but a new standard developed by VESA sets the refresh rate at 75Hz for monitors displaying resolutions of 640x480 or greater. This means that the monitor redraws the display 75 times per second. The faster the refresh rate, the less the monitor flickers.

Flat-panel
Plasma
CRT (Cathrode Ray Tube)
LCD (Liquid Crystal Display)
HPA (High-performance addressing)