If your SD slot is big enough that a card to go through it that's a SERIOUS defect and you definitely need to get a new one. If you really can't get to a BN you could call and tell them what happened, and demand an exchange with a new SD card for the one you lost.
If the card and data are that important, I think I would make the trip to a B&N store. Maybe they could take the back of the NC and get your card out.
If the files you backed up are B&N content, they are stored on B&N's servers and would re-download once you got your new NC set up. If you haven't done so, you need to deregister the defective unit before you send it back.
You can also try connecting the NC to your PC and copying the files that way.
There's always the option of tearing into the unit yourself, but I'm pretty sure that would void your warranty.