As wkw427 suggested, the USB Controller inside the enclosure may have failed. You can remove the HDD from the enclosure and attach it internally to a desktop computer, via a
USB Adapter or putting it in another
USB Enclosure with a Power Adapter.
To recover your files, you can use the totally free
TestDisk I have had the best luck with
GetDataBack. You will need another drive of the same size or larger to restore your files to