hmm..if they still do them the way they used to, the LCD screen has 2 connections inside; the signal, and then the power. Back in the Day (I fixed laptops from the original Compaq Portable to the..uh..dang, about '97 or so, and have done work on IBM T40's..;) they actually had a little backlight, that was a tiny florescent light the length of the screen. It's possible that maybe the connection is loose, and they can reseat it. If it's gone out, then you're looking at a new LCD screen. I can tell you it's the most expensive piece of the laptop, even including the motherboard.
Sorry to be such a 'bundle of joy'. I'm actually slated for Dell training, if my @#$ing PIN number (yup, even techies have to get them) ever shows up. Used to work on the desktops back in the Day (GX1's, etc), but it's been awhile..;)
here's something to try; plug the video cable into the back, and see if you get a signal. If not, it could be the system board; if so, it looks like the LCD. If you see a flicker of light when you turn it on (i.e., the screen lights up 'slightly') the power part may be ok, and the LCD portion (the really spendy part) might be it. If no change in the lighting, then it's likely the power supply
Well, on the bright side, at least it's not stolen..;) good luck, hope this gives you enough to go on getting a repair done.

I wish I'd said that.. The Staircase Wit

anahl nathrak uth vas betude doth yel dyenvey..;)