|1- If you have access to it at all or at least it shows up in 'Computer', try running Recuva on it.|
2- If it shows up with a drive letter but that is all, try testing it with Seatools from Seagate. Run the longest test.
3- If it does not show up in 'Computer', go to Disk Manager and see what it shows there (report this back). See if you can assign a drive letter to it (right click menu). If it shows in Disk Manager but you cannot assign a letter, you may need to partition it and Format it (quick format), then try Recuva to see what can be restored BUT, hold on this for a while to see if anything else works (a last resort that has worked for me before).
4- If it does not show up at all in Disk Manager, look in Device Manager and see if it is showing at all, report back results.
5- If it does not show up anywhere, you may need to remove it from the external case and install it as a second internal hard drive (plugged in, but not mounted) to see if the drive itself works at all (proving that the problem might be with the case). If it shows up as an internal drive, try to access it, and if needed, try all of the above on it now.
Report back results.
You have to be a little bit crazy to keep you from going insane.