I had a 17-inch LCD monitor that did this to me. Press power button, picture for about a fraction of a second, then nothing. Bright, intense light put to the screen revealed that there was still a picture, only no backlight. I replaced two vented capacitors inside and the display works now. Here's the eHow article I wrote about it:
http://www.ehow.com/how_5086953_repa...r-monitor.html