I have tried two different cables. One is purely a USB cable (and is the original), it connects to the computer for mass storage fine; but not charging. There is a separate cord that is purely for wall outlets. It charges fine. Then there is another one that fits my phone. It connects to the computer fine for mass storage, but doesn't charge. It comes with an adapter to turn it into a charger for wall outlets. It charges fine when I plug it into the wall.
It doesn't seem to be the cable at all.