Can you see any faint images on the screen?
My Dell LCD had a similar issue where one of the transformers on the backlight inverter had fried. The backlight would work for 2 seconds after powering it on, then stop, however you could still see a faint image of anything being displayed.
Replacing the inverter fixed the problem, I don't think it was cost effective but it enabled me to learn about things in the process which was more valuable to me.