Most likely, either your backlight or power inverter is damaged. This is textbook power inverter issue.
Plug the laptop into an external monitor. What happens?
Power inverters usually run anywhere from $50-$100 - you can find good deals on eBay from sellers with good feedback. Find the one for your model monitor, install it, if all is fixed - great. If not, resell the sucker on eBay for the same price or more.
Or, bring the laptop to a repair shop and pay them $300+ to do it