Two possibilities, the i/f to the HD itself is bad or the HD doesn't have the enough power to mount. Of course, the HD itself maybe bad. It sure looks that way since you've swapped it out to another ext. case. The last test is to simply mount it as an int. HD and see if it gets displayed(mounted) with proper hook-up. It need not be the be fancy just jerry-rig it to test. If it still shows unmounted, the HD is bad or badly corrupted. You can try the diags from WD to see what the results are.
I have an external hard drive but it wont show up on my computer (including the disk management section of computer management).
I'm running a gateway p-7805u with vista and the hard drive is the inside of a western digital Mybook. The power supply failed, and I took it apart to put the drive in a StarTech external HD bay.
When I plug the HD into my computer (via usb or but not esata) it makes the noise the computers make when something gets plugged in. however, I cant find it anywhere.