Ok so it is turning on but the display stays black? Is this right? If that is the case the first thing to try is... turn off the laptop, connect and external monitor, then turn on the external monitor and finally turn on the laptop. Can you see your desktop on the external monitor? If yes, then you will need to check thelaptops ribbon cable (it connects the display) and if that isn't damaged you may well then need to replace the actual display.
If you can't see anything on the external monitor (but again are sure the laptop is turned on) then your graphics card is probably going to need replacing.