One of the websites that offer MacBook repair is powerbookmedic. I think you can find the parts you are looking for and they also have comprehensive guides where you can see how to open and replace parts of your macbook.
Some of things that could go wrong with the screen would be the screen itself, the logic board or the cables. Since you mentioned that it works fine with an external monitor, the logic board must be ok. So that leaves you with the problem either being with the screen or the cables.