Solution: In that case the reason why the external HD (e.g. a WD / Western Digital Elements 2 TB) is not recognized by the OS might be a corrupt driver store. Perform the following steps to get that issue fixed / solved:
1.) Attach the device to the PC where you have the issue with
2.) Select the unknown device in the device manager, right click on it and choose uninstall (this ensure that the OS need to recheck for the drivers the next time. Otherwise the cached false detection is used!)
3.) detach the device from this PC
4.) Open Windows Explorer
5.) Go to C:\Windows\System32\DriverStore\FileRepository
6.) Search for folder which begins with usbstor.inf
7.) Open it (if you have more than one, choose the most recent)
8.) Copy "usbstor.inf" and "usbstor.PNF"
9.) Paste those two files to C:/Windows/inf
10.) Reboot your pc fully
11.) connect the HD to your PC
The issue should be solved now
You need to have administrator rights on the PC where you wish to perform that
It seamed to be that some USB 3.0 driver caused the issue and deleted the files during the installation. Sometimes the driver installation also failed, but as various other USB devices works most users didn´t care about the error message they got.