Have you tried it on another computer to see if it gets recognized? Another pc in your house or a friend's pc?
What usually happens with external drives is the sata to usb interface goes bad and although the status on the drive itself is good, the drive itself works, your pc just can't read it because of the bad interface.
If this is the case, what you may need to do is get a new enclosure for it, they are pretty cheap, somewhere around 20 bucks usually.