|See if Disk Manager will let you reassign the old drive letter back and see if that might help.|
Try removing it from the external case and install it as a second internal hard drive (plugged in but laying on the top or bottom of the open computer case) and see if Windows recognizes it as formatted. If it still needs to be formatted and the drive letter it assigns is not its original letter, try reassigning that letter and see if that helps.
As a LAST resort (do not try until all other options are exhausted):
Format the drive but make sure that you use the Quick Format. Then run a file recovery program like recuva to try to restore the files on the drive. Understand that even the best recovery software will may not be able to recover everything (which is why it is a last resort). I have seen that common files like Music, Pictures (JPEG), and common Office files (Word, Excel) are more likely to be recovered than less common file types (Photoshop, Autocad, saved games, etc).
As mentioned, always save important files in more than one place. External drives are best for backing up important files that are on computer's internal hard drives and for taking those files with you. If you modify a file, make a copy on a flash drive until you can copy the new version back to the computer. If you off load files from a laptop to make extra room, place a copy of them on a desktop or make a CD or DVD archive copy to put away BEFORE you delete them from the laptop.
You have to be a little bit crazy to keep you from going insane.