look close to the screen and see if there is a faint picture. if there is then read below for the issues and solutions that can cause this problem.
Issue 1: Lid button sticking
this is a common issue with this model that the lid button sticks closed. fiddle with it to see if it opens and the light comes on.
issue 2: Inverter for the monitor is bad
this is not to uncommon an issue when this problems shows itself. Laptops
monitors light up with a fluorescent bulb. This is powered by an inverter. These can go bad and if they do the light will not turn on. you need to take this to a service station. i don't recommend trying to replace without knowledge of this. They are high powered and you can hurt yourself or damage the screen
issue 3: fluorescent bulb went bad
this is usually the least common but could have happened. usually happens when peopel spray their screen with cleaner and it drips down inside the bottom. This can be fixed by a service center but coudl get costly. best bet is buy a new screen.