Apple does not readily supply backlights or other apple parts (aside from ram or processors when applicable) to average citizens, as self-service would most likely void the warranty on that or another part.
Buying a third party replacement screen is also not recommended, as third-party screens
A: are not trusted to work and may fail quickly/not work at all
B: are not covered by the machine's remaining warranty/apple care
C: require self installation or ACT installation that may void the product's remaining warranty.
If you need a new screen (as it would sound that the whole screen needs replacing anyway) I would definitely take that machine to an available Apple store Genius Bar.