Find a program that creates an images on the sector level of your hard drive. That way it doesn’t need to bother with reading the beaurocratic part of the data. There’s backup programs out there for that. You might need to plug it into your PC directly instead of USB, and the program might be needing to be installed to run before windows boots up. Then find another program that allows you to look into that image file.
There are ways of saving data from a potentially corrupt drive, but it needs a bit of research. I don’t know from the top of my head and I haven’t even had my coffee yet.
This probably wasn’t too helpful, I’ll try again.
First things first, remove the hard drive from the enclosure and put it directly onto your motherboard. You do not know if it is actually the disk that’s faulty, or if it’s the enclosure. Without finding that out, any steps taken are premature.
Second … this might help:
Report back and share every output that equals a roadblock for you. : )