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