Unfortunately you have done what so many people do - or rather don't do. You have not kept your precious files backed up on a second drive. Never, ever save your data on just one hard drive because it can fail at any time.
With any luck, the only part that has failed is the SATA/USB Bridge Chip inside the enclosure (it's a small PCB). If you can extract the hard drive from the enclosure and remove the bridge chip, you may be able to fit it inside a third-party enclosure and plug that into your PC, then cross your fingers.