I used to do IT support for 7+ years... Do not waste your money purchasing recovery software. (Recuva's free version works amazingly well, anyway.)
I would go out and purchase a cheap SD card reader before I purchased any recovery software.The primary issue you're having is the card itself is not being read. This does not mean the data is gone on the card itself. Most likely, the controller (which lets the computer and SD card's storage space "talk" to each other has failed or is acting up.
Before any of these suggestions, find an eraser from a pencil and rub each of the contact sensors... That's resolved issues with several chargers, ink cartridges, SD cards, and more that I thought had failed forever...
Some other ideas:
(1) Try to go into your Device Manager and uninstall anything related to USB ports. Restart.
(2) Go to Computer Management (right-click on Computer > Manage). Pick disks on the side. Insert it; see if anything pops up. If it shows, but doesn't actually show a number for the storage space, there may be no hope.
It's extremely unlikely to fail... I do photo shoots on the side and even though there's hundreds of dollars on the line after each shoot, I never think to back stuff up right away. They're highly reliable and most likely, it's just the contact sensors or the reader slot, not the card itself. Most built-in card slots are @#$%&.