Going to buy a new cable, but it seems odd that it works just fine in the 2.0 ports, but not in either of the 3.0 ports. If the cable was bad, it would seem like it would have the same issue plugging in to a 2.0 port. As I said before, the "power" light does come on but does not make a connection. Could it be there's not enough power coming from the port, to make a good connection? If the new cable doesn't fix the problem, my next call is to Alienware support! It is under warranty!
I assume that you are using a USB3.0 cable, which would mean that it has the extra little bit on the HDD side of the cable.
If the cable is faulty and one of the "extra" pins is the damaged one, then it would explain it working in USB2.0 ports and not the USB3.0 ports.