I have a Dell 19' inch LCD moniter.
The screen would display for a few seconds and then the backlight turns off. I can still see the images if I use a flashlight close up. Powering off and on will display it for a few seconds before again turning the backlight off. I suspect the inverter is the culprit but after inspection I see no issues.
Check the capacitors on the power supply board (if you can get into the monitor without damaging the case).
Failure is pretty common through I haven't heard of Dells going-- evidence may be visible (bulging or leakage) or may not be. If you have a soldering iron, replacement capacitors are cheap and simple to fit.