Mount the card in the adapter, then plug that into an SD card-to-USB adapter and put the card into your computer. Download
PhotoRec - CGSecurity burn it to a CD and boot the computer from the CD. Aim PhotoRec at the SD card and let it recover whatever is recoverable. (It will recover any block of data that looks like a file or piece of a file - assuming that it's not the controller in the card that went bad, in which case the card is now just a piece of plastic, epoxy and metal, and putting the memory chip into a working card would cost about the same as a new luxury sedan.)
Then, unless it's a SanDisk card, break or shred it (so nothing can be recovered from the memory chip) and buy a SanDisk card. If it's a SanDisk card contact them - they'll usually replace it with no problem.