It sounds like you may have a back-light or inverter problem. If you are comfortable troubleshooting your laptop hardware, here are some suggested steps. This link might be helpful in determining which issue (if either) you are dealing with.
Below is additional troubleshooting steps you may try – good luck.
Problem: The laptop turns on, LED lights on the laptop turn on, cooling fan works but nothing appears on the screen. The screen is completely black and blank. There is no image on the screen at all, not even a very dim image.
This problem could be related to the memory failure. It’s possible one of the memory modules failed and the laptop doesn’t turn on because of that. In this case you can try reseating memory modules to make sure they are making good contact with the slot. You can try removing memory modules one by one and test the laptop with only one memory module installed. You can try replacing memory modules with new modules.
– If reseating/replacing memory modules doesn’t help, try removing the hard drive, DVD drive, modem, wireless card, keyboard, etc… In other words, disassemble the laptop to bare minimum and test again. If the laptop still doesn’t turn on, most likely you have failed motherboard or processor.
Another thing to try would be to connect your laptop to an external monitor with a VGA/DVI or HDMI cable (your laptop is bound to have one of them). If it doesn’t work on an external screen then it could be graphics card failure as mentioned here.