Your monitors backlight is shutting off due to a failed component. The inverter circuit which drives the high current CCFL backlights, has a feedback design so that if there are any problems with the devices along the high current path, the high current will shut off. This way if something got shorted out, it would not sustain or cause any great harm. This is a great feature if you are the "short" in the circuit.
So in actuallity, your monitor is still on, and it's still showing you a picture. You just can't really see it because the light from behind has turned off. If you take a flashlight and put it up close to the screen, you'll see your desktop again!
As to what is causing this, It can be several things.
-A broken or burnt out CCFL
-A bad capacitor in the power supply filter or on the inverter.
-A shorted out IC.
-A mouse has crawled inside your LCD and chewed the CCFL wires. (this usually is accompanied with a high pitched squeeling sound, and/or smoke)
You can send me the entire monitor and I will repair it for $40. You pay shipping costs BOTH ways. Let me know if you're interested and I'll provide you with more information on where to send it.