It could be one of three thngs - in order of likleyhood:
LCD Screen Backlight - rather like a small fluoescent tube that actually lights up the screen.
The Inverter which basically changes the current to suit the backlight.
A loose connection or broken wire from the motherboard to the screen - these wires usually run upto the screen close to the hinges and may, after being gently twisted every time you open the lid have simply snapped.
In any event you have two choices. Have a look yourself for anything obvious by dismantling the computer (Not recommended if your laptop is under warranty or you are not technically minded). Take it to a Laptop repair specialist for a quotation. Be warned though any sort of repair is likely to be expensive because spare parts for laptops are too!