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There are a few different problems which can result in that behavior.
1) Faulty LCD power inverter
2) Loose cable
3) Bad graphics card (if dedicated)
One of the most common poblems is with the screen backlight power inverter, you can check for that by shining a bright light at the screeen when the computer is on and seeing if there is a faint image on the screen. If there is, the power inverter needs replacement. On some models, it can be replaced by itself, on others the entire screen must be replaced.
Another common issue is a loose video cable. Sometimes that can be checked for by altering the angle of the screen. If you get a picture with the screen at a certain angle only, likely a loose cable.
Those are good starting places I think.