My monitor screen goes black (perhaps the monitor turns off like in screen savor mode). I can turn it back on by doing this: pushing the off BUTTON, waiting about 5 to 7 seconds, and pushing the on button. It does this about 5 to 10 times/day, and is getting more frequent from a month ago when it was 1 or 2 times/day. My monitor is a Dell refurbished 19 in flat panel, about 4 years old. My OS is Windows XP and the computer is a Dell Dimension 4600 series, 2.4 GH, 1024MB Ram.The only 2 things it could be are the monitor itself or the vid card/onboard video....
Try the monitor on another machine to see if it's the culprit.
And to test your video try a different known working monitor on your machine to see if the vid card is the culprit...I'm not sure what kind of lifespan LCD's have, but it MAY be going south. First of all, you should make sure the cables are properly seated. Turn the computer off, disconnect the cables, wait a minute, and reconnect them securely.

The fact that turning off the monitor fixes it makes me think it has to be purely a hardware issue, probably electrical. There's a good chance it's not getting the proper power. I have a feeling this monitor is going to bail out on you soon. You can either take it in to get it fixed or replace it. I'd replace it.

It's possible that the video card is to BLAME, but I'd bet on it being the monitor. You should, of course, test out a different monitor first just to verify this.I had this exact same problem and my graphics card was wrecked. To be 100% sure take out your graphics card and turn the computer on and see if the monitor turns of, if not then its your card, and also put your card into another computer and see if it happens then.
What i did was when i had the same problem, i took my card out and put it in my friends computer, and the same *censored* STARTED happening to his computer. If you don't have another computer to check your graphics card on, just take the card out and turn on the computer and the computer should work with its onboard card.

YOUR CARD IS PROBABLY BUSTED Alex if they remove the video card of course the monitor is going to be off...It wont be off if its got an onboard card.
Kermir should check if his graphics card works on another computer, thats what i did and same thing happened.Before going to a HECK of lot of trouble, be sure to check and/or reset the power and screen saver option.