These units have two parts: the HDD, which is nothing more than a regular HDD with a SATA connector. The second part is a simple SATA-to-USB converter.
And there's a cable, too. Any of the parts can fail.
First, try another USB port, then another cable if you have any reason to think it got damaged. Try another computer if you can.
Beyond that...the device's internal USB converter can fail, and they do, but most often the drive itself is bad. They get dropped, kicked and abused, and the cushioning is bare-minimum.
The only way to troubleshoot this thing is to tear it apart and separate the pieces. But first, call Western Digital support. In my experience they'll honor a warranty if a professional shop takes it apart, and you call them first.
Once it's apart, it's a simple matter to test the drive by attaching it directly to a SATA port or a known-good USB converter.
-John