Your description doesn't make it clear (to me at least) just exactly what happens when you connect an external monitor and toggle the display. Do you, or do you not, get a proper video display on the monitor. If not, then the problem is probably the display subsystem itself. I don't know whether this particular notebook has the video integrated into the MB or whether it uses a daughter card. If it's a daughter card, then a replacement might be economically feasible.
If you DO see a proper video display when connected to the external display, then something is wrong with the LCD itself. Try booting the system up and looking at the screen from various angles under low light and bright light conditions. If you can discern that a display is being formed, but that the image is just too dark to be seen easily, then the problem is the backlight which is one of the most likely points of failure, and also one of the cheapest possible. They'll only charge you an arm-and-a-leg for replacing it. (With labor included it will probably cost somewhere in the same neighborhood as a new daughter card, depending upon the type of graphics subsystem.) Replacing the backlight might sound like a simple thing to do, but it isn't on most notebooks of my acquaintance. They don't build these babies for ease of maintenance. If there is no patterning on the darkened screen to indicate that an image is forming, then the failure could be as simple as the ribbon cable (or one of its connectors) that carries the video signal to the screen. It could also be a catastrophic failure of the screen itself. The cable / connectors might not cost much at all to get replaced. A total screen replacement will certainly cost more than the computer is worth, from a strict cost effectiveness standpoint.
I hope you get it sorted out.
- prosaic
PS: Did you check the manual (or just check out the keyboard / controls) to see if there's a brightness adjustment on this thing? No, it's not likely that it can be set so low that you wouldn't be able to discern the desktop image at all, but adjusting it to the extremes might get you some differential diagnostic information if there is a partial failure of the backlight system.