Can Nintendo repair my Nintendo DS?

I gave my old Nintendo DS (the original, not Lite or DSI or anything like that) to my girlfriend and it fell and broke.

It still works but it’s VERY FRAGILE right now. The hinge that connects the dual screens is hanging on by a thread.

I was wondering if I would be able to ship this to Nintendo (I still have the box and everything) and have them either repair it or give me a new one. I had some experience with this back with my Gamecube. Even though the Wii was out and popular, I was able to ship my Gamecube because I had the box and have them repair the disc reader. I was wondering though if they would still be able to fix this since it’s a physical issue (i.e. parts of it cracked open and so the plastic pieces are lost, I think)