Also, the symptoms of this connection problem are that the cable only charges from my new MBP at this point, and the cable has to be placed carefully in a certain position or I don't get a connection. Does that mean it's absolutely the cable or could it be a connection problem with the unit itself? What's the most likely scenario?
The most likely scenario is that it's either one or the other...or something else altogether.
Your external HDD connects via USB; try it in all of your USB ports and see how/if it works.
(What, exactly does "
the cable only charges from my new MBP" mean?)