The back plate of a New 3DS XL is a bit tricky to take off because of some plastic clips. I suggest looking at some YouTube videos on removing the back plate and replacing the shoulder buttons. These buttons often break because of the pressure when they are dropped on the corner. Here is a video I suggest watching:
https://www.youtube.com/watch?v=VbK318ONhSo
Here is also a video on how to take off the back cover, which is a bit tricky:
https://www.youtube.com/watch?v=H-EKuPe0jtQ
Did you ever drop the system or have accidentally gotten water on it?