You don'd give too much facts to give educated guesses, do you? Like, can you see anything at all on the monitor, or is it black right from the start? Or does the power led turn from orange to green? Or does it say something like "no signal" on your monitor - or "out of range"? What OS do you have?
So, if there are no signal lights or messages on the screen, check all the cables are tightly seated and make sure the monitor is on. Check the monitor with another computer or check your computer with another monitor. Or both...
Check that all components inside the computer sit tightly in their places and that their contact surfaces are clean. A loose CPU cooler fan wire can prevent booting, so does a loose memory module or video card. Get rid of dust bunnies and other debris than can clog ventilation holes or prevent fans from rotating.
If you can see the POST message, tap F8 to see Startup options. Try to boot into Safe Mode. If your OS is Windows XP, you can also try VGA Mode, where you can set the monitor options to modest enough. Ensure your refresh rate is set to 60 Hz. Reboot.
Hope this rudimentary check list helps.