This is one of WD's USB native drives which has no SATA port. I'm afraid that if it's not recognized now it'll need professional recovery. You can't even hope to accomplish anything by removing it from the case (although I'm sure someone's going to suggest that after I post this).
Hopefully the issue is just related to bad sectors or some minor firmware corruption caused by the movement while it was running. In such a case the cost for pro recovery may only be $300-500. If one or more of the read/write heads have failed then you'd be looking at $650+.
Where are you located? Perhaps I can recommend a place that's not too far away from you.