Well if it is the experiance you want, I would start looking for an identical computer, as long as the lcd lights up (screen) anything else you should be able to replace. (I would look on kijiji around here, or the local equiv in your area) People will give stuff away because they hate to throw it out, or sell it very cheap. I would take the screen in for testing though, perhaps it is just something simple like a small crack in the IC board that could be soldered, or you could even open the screen yourself and look for a crack. They would be hard to see, but with 3x reading glasses (got mine at the dollar store for reading IO circuits) it should be possible. If your laptop has a video out (such as s-video) connector, you could connect it to a tv and see if that works. Thats an if though, since I dont know your system. My suggestion at this point, before putting everything back together, inspect the components closely, (pay attention to capacitors to make sure the tops are flat not rounded and around the screws (look for cracks)). Make sure everything is firmly in place as you are putting things back together, particularly the video card (unless it is onboard) recheck the connections and the power to the display. From whay you have been saying, and from replies to other posts, I think we have the issue narrowed down to the video card, connectors, or the screen (or power to the screen). I always try to eliminate the least expensive things to repair first.
Aside from what I mentioned above, without seeing the physical components, I can only toss out maybes.
O M G!!! I was just thinking... and I hope this is not the case... is there a fuse to the video? Like in the back of the screen on the IC board? (would be a glass tube fuse, a small square green resetable fuse (could be a toggle) or a resistor like part (single colored no stripes with an F on the circuit board) It would be a kick in the head if it turned out to be a fuse. Particularily, if it was a glass type fuse a jar might break the filament inside. Something to look for anyway.
Hope this helps or give you some ideas.