|If you have been seeing an overall tint to the display for a while before this first happened, e.g. pink - your backlight is probably in the process of burning out.|
Sometimes when that is going on, the voltage inverter "senses" there's something wrong with the backlight and automatically shuts down it's high voltage to the backlight to prevent damaging the inverter - hence, blackness.
For some info about replacing a voltage inverter or backlight, and what some typical symptoms are, see response 5 in this:
The backlight in an LCD display on a laptop or an LCD monitor has a finite life, just like other florescent bulbs do, and typically it doesn't last anywhere near as long as a CRT display.
Plasma monitors, or Plasma TVs with monitor inputs, on the other hand, have an extremely long rated life.
The lower you keep the brightness on an LCD monitor, the longer the backlight will last. It also helps a lot to use a screen saver or Power setting that turns off the monitor display completely when you're not actively using the computer.
If you get another LCD monitor, the backlight in better quailty brands tends to last a lot longer than it does in cheaper brands. E.g. a friend of mine has two Samsung LCD displays - a 19" monitor about 5 years old, and a 19" LCD TV about 4 years old she uses the monitor input on most of the time - they are still fine. Up until about a year ago, she had them on 24/7 most of the time. She still has them on 24/7 most of the time, but the computer is set so it turns off the monitor displays completely when she's not actively using the computer.