Now it's time to really look into things. First suspect is the SD card. Slip it into a PC and see if it can detect the SD card.

Is it blank? Does it refuse show up? If so, there is probably an issue with the card itself. See if you can find/buy a spare one, and copy over any backup you may have made beforehand.

Does the computer read the SD card? It may be time to crack it open and replace the SD card reader.

If you're really squeamish about cracking things open before knowing for sure, try another SD card in the 3DS. The card you're using may just be faulty.