OK. I am assuming your laptop has an LCD screen and uses a CCFL for backlight. I am telling you the procedure I follow to isolate the failure.
If you can see the image when the laptop is attached to an external monitor or to TV, then the graphic card is working fine. In other case you would have to buy a replacement mainboard.
If you see no image at all but the screen is turning on and you see a WHITE SCREEN and light coming from the bottom of the screen, then both the inverter and the screen's CCFL are OK. Check the flat cable in the back of the screen. It should need to be reattached.
If you had a BLACK SCREEN, the you should find out which of these parts is failing, or even the cables that connect the mainboard to the inverter and the one that goes from the inverter to the screen (the connector with the white and the pink wires). Borrow an working screen (doesn't have to be the same size for this test, just the same LCD technology) and connect it to the inverter. If now you have a WHITE SCREEN the inverter is OK and the screen needs to be replaced. If the new screen is BLACK too, then the problem is the inverter.