Well if its black it could also mean the Power Inverter for the backlight is out as well.
have you tried pluggin it into an external monitor? Try that first and see if you get anything (May have to use the FN key and the Key that switches between External and Internal monitor to get it to work) But if you turn it on, and kinda get the glare out of the way can you see an image at all? Because if you can then its the power inverter.
If the backlight comes on but its just a black screen, and the external screen works then its the LCD screen which you can get here
http://www.laptopscreen.com/English/model/Sony/PCG-71912L/
Bought from them MANY times. Great price, Brand new.
If the screen doesn't show anything, and the external...