Connect it to a different computer.
If it works, then connecting to _your_ computer is the problem.
If it does not work, then either:
* the USB-to-disk-drive adapter inside the casing has failed, or,
* the disk-drive inside the casing has failed.

Open the case, and remove the disk-drive, and connect it as a "slave" disk-drive in your computer, to see if the disk-drive itself is "good" or "bad".

Google-search for "Data Recovery Services" -- these are commercial, high-cost, companies, that can temporarily repair a "dead" disk-drive, just long enough to try to copy all the files from the disk onto a new disk-drive.