To check the display, connect your system to an external monitor to see if you can see your desktop image on the external display, next take a flashlight and holding it on the screen of your system at an angle see if you can see the faint outlines of your desktop icons.
So if your external display is working and the flashlight test also lets you see your desktop you've isolated the problem down to the backlight circuit. Just to be sure we're on the right track here
OK, so here's the deal there is a chip on the logic board which converts the batteries (DC) power to the correct voltage the backlight LED's require. There is also a fuse link that can pop as well. Often these get damaged from getting the system wet so if you remember sitting your system down on a wet surface or having something spilled on it that could be what did you in here.
If you didn't get your systems wet:
While its possible a single LED or a string of LED's go down which would be more noticeable. A completely unlit screen often points to a burnt fuse link and the ribbon connection inside the lid could be damaged. Often I see a dented lid cover as the root cause here. Did you bang your system or sit something on the lid?
So if you open your bottom cover you can see if the inverter chip is bad it is often visibly burnt. Here is a picture of the logic board and the blue outlined chip is what you want to look at: Logic board. The display ribbon cable connects to the logic board just to the left of the Yellow marked chip at an angle. The fuse link is the little component just above the Yellow chip which has a P marked on it. Yours may have just a dot marked on it.
Also do you see any staining or corrosion? Just in case you forgot you got the system wet at some point. Look at the ribbon connectors solder joints as often I see corrosion there.
Are you able to isolate what happened?