Hi there LP14,
As the HDD is not recognized by Disk Management but works just fine on other systems, then I guess this should be drivers related issue.
You can go to Disk Management -> Uninstall the drive -> unplug it and reboot -> plug it back in and see whether it will appear.
In case the issue persists, I would advise you to reinstall your USB 3.0/2.0 drivers. You can find them on your MOBO's website.
Have you tried using different ports? If you haven't, you can try the ones on the back of the computer case.
Cheers,
D_Know_WD