Hey OP, was your machine part of the ambassador program? Nintendo can't get you anything back to you except that. I lost my 3DS (or it was stolen, I don't know), and I picked up a used one for cheap. I called and talked to Nintendo, and since I still had the original box for my first 3DS, I was able to cut out the code and mail it to them as proof of ownership, and they enabled my new 3DS so that it could access the ambassador games for free... they didn't really mind that it was used.
The only good thing that came out of this was that I was able to get the Zelda edition 3DS for $115 from a pawn shop
I didn't get the couple of eShop games I'd bought though -- they saw them on my account but assured me there was nothing they could do.
You might have to press them a bit to get this--I'm not sure. The person I was on the phone with said it was kind of a unique case (at least it was at that time), and they went and talked to people higher up who allowed for this to work out
Also: like others said, definitely take it to GS. They will take some fucked up shit. Take it into them when they are doing a nice big bonus on hardware trade ins... if you're willing to wait you could trade it in for XL