If the screen backlight or inverter has failed, then the screen will be displaying an image but it will be very, very dark. Could you try looking at the screen very closely under different light conditions to see if there is actually something on the screen but it's just very difficult to see?
Another possibility is that the graphics card is trying to send the signal to an external monitor rather than the built-in screen. There is usually a Function key sequence such as [Fn] + [F5] to switch between the internal and external display. You'll be able to tell if you have this option (most laptops do) because one of the Function keys will have a picture of a monitor or it will often say "CRT / LCD" on it.
Hope that helps
