1) Video cable:
A) Video cable connection on motherboard side is loose, and/or on back of LCD screen.
B) Video cable is damaged.
2) screen Inverter:
screen Inverter is bad.
3) LCD screen:
LCD screen is bad.
4) Graphics chipset:
Graphics chipset is bad.
Suggest you connect a VGA monitor to the VGA port (Connector) on your laptop.
See if the problem is the graphics chipset, Or video cable, Or display assembly.
You didn't state what manufacturer and Model Number of laptop this is.
All I can do is state generic information.
This is an example of a VGA Cable, and VGA connector,http://en.wikipedia.org/wiki/VGA_connector
The VGA connector will be on the side, or back of your laptop.
For the VGA monitor you can use a CRT type monitor, (Looks like a small TV), or a flat LCD screen monitor that has a VGA cable.
Laptop OFF, monitor OFF, connect the external VGA monitor to the laptop.
Turn the monitor on. If a CRT type allow it to warm up.
Turn the laptop on.
By default the display should show on the external VGA monitor.
There are at least 3 display options.
1) Laptop internal monitor ONLY
2) Laptop internal monitor AND external VGA monitor
3) External VGA monitor ONLY
Press, and hold down on the Fn key, and at the same time tap once on the Display Toggle-Over key.
(For an example HP's usually use the F4 key for a Display Toggle-Over key)
Display shows the same on the external VGA monitor?
You have a bad graphics chipset.
[ Some laptops have been erroneously stated as having a graphics card, when in fact they do not.
The GPU (Graphics Processing Unit) is soldered directly to the motherboard.
This is Integrated Graphics.http://en.wikipedia.org/wiki/GPU
There is no changeable, replaceable graphics card. Therefore the solution is motherboard replacement ]
IF, the display is good on the external monitor, you have a problem with the Video Cable, and/or in the Display Assembly.
After diagnosing with an external VGA monitor, post back in a Comment.
Also post the manufacturer name, and model number of the laptop.