I fixed a laptop with that issue earlier this year. Theres a couple things that could be the issue here.
1-LCD screen is bad(unlikely but I've seen weirder things)
2-The LCD bulb is bad(This is not the technical term, I forget what it is but if you google, you'll find the answer, or even if you want me to do it for you.
3-the LCD inverter cables(LCD to inverter, or Inverter to bulb) is disconnected or burnt.
4-The LCD Inverter is bad/burnt/disconnected
Now, this is not an easy fix. You need to be comfortable working with tools, understand proper grounding of yourself so not to blow the laptop to bits, and be willing to risk about 100-200$ depending on the route you take to fix this.
Unfortunately, the only way to test this kind of issue is in this order
1.a-Plug the laptop into an external monitor through the VGA(blue squareish looking port in the back), boot the system, it should display fine on the external monitor.
1.b-If it doesn't work, we have a bigger problem than just the screen, it would suggest the video card itself is faulty or damaged. If it works proceed to step 2
2.a-Open up the LCD cover, confirm the cables are connected, confirm that the inverter(a rectangular looking chip with a cable plugged into each side typically on the bottom side of the screen as it is what controls if the screen is displayed or not)
2.b-If you suspect the Inverter, you will want to move it towards you and away from you and it should provide the result of the screen coming on and off.
2.c-If you suspect the inverter cable, look for burnt marks or disconnected wires, possibly even the connections just being loose.
2.d-If you suspect the bulb itself to be bad, you unfortunately can't just glance at it and know it's bad, it's super thin and it either works or it doesn't, and more likely the issue is the wires that connect to it on each side of the bulb.
Again, if you are not technically inclined, I do not encourage you to attempt this on your own. You will need someone who knows how to solder, connect and reconnect thin circuit strips(which tend to break easy). This will cost a lot if you don't have a techy friend to help out.
Simple Solution(really expensive)-Buy a new LCD Screen which comes with everything preinstalled, and just remove the old and install the new. Make sure it comes in the casing and everything so you just screw it into the laptop base and connect the cable to the motherboard.
Cheaper Solution(sometimes)-Have a techy friend do and research the things I suggested up there, the problem could be fixed in the price range of 6$(the inverter),6$(The bulb), 10$(the inverter cable),100$(The screen)
Good luck! and yes I wish I could provide pictures and step by step stuff. But this kind of helps.
http://www.screentekinc.com/lcd-removal-instructions.shtml