I gather it is still under warranty?
Here is a list of Data recovery software that might be of use : https://en.wikipedia.org/wiki/List_of_d ... y_software
I use one that is not listed there called R-Studio which is very good. But from that list that Data Lifesaver
looks interesting and may work over USB.
Aren't those WD My Book drives just normal hard drives in the custom container? If it's not under warranty any more it might be worth just cracking open the case and accessing the hdd directly, bypassing any thought of it being the cable. If it is under warranty, though you still have to weigh up the option that WD will somehow fix it without destroying the data or just by replacing the hard drive.
Basically you need to ask yourself what is worth more, the data on it or the warranty?