If you have a desktop computer handy and are careful enough to get the hard drive out without damaging it you could try 2 things.
#1 move the hard drive to a new USB enclosure and maybe it will work if the USB to SATA controller is shot on the enclosure that the original drive came in.
#2 remove the hard drive and mount it onto a spare SATA port on a desktop computer, and if the drive is healthy, but the enclosure was bad, you now would have access to your data.
Based on success or failure of one of these methods, if your still not able to get access to your data you could try a trial of a program called GetDataBack NTFS. If the drive spins up and the HDD controller isnt toast, this software can reassemble lost file systems and tables and allow for you to send the data to a healthy hard drive. But this software costs money to recover data. So I suggest trying trial first if this is a method you need to use, and see if it locates your data. It will show file names and directory tree info etc so you know its found your data, but the trial will only show your data, they dont allow recovery of data with the trial, just proof if the software can or cant recover it. I have used this software on many damaged or corrupt drives.