Bad news. You can't retrieve your saves from the SD card and reuse them. They're on your card, but the only system that can recover it is your busted N3DS. Had you made backups of those saves in their
decrypted form using Checkpoint or JKSM app before it broke, you would have been able to transfer your game progresses on your replacement system. Sorry bud.
If there's any counseling, you can borrow other people's saves or try to recreate your own depending which games you've played have save editors.
Look in
3DS - ROM Hacking, Translations and Utilities to see if whichever of your individual games has a dedicated editor.
There are threads scattered about with shared save files, so not any one can be named. Try also looking in
3DS - Games & Content.