I took it to the Verizon store. They suggested the problem might be due to a crack in the side of the shell, and that it was affecting the internal connections...so I got the phone replace via insurance.
So, obviously the new phone has a new micro-USB, and that works for charging. But I just spent 45 bucks on a wireless charging pad.
Low and behold, it didn't work with the new phone either.
I, too, got the items via Amazon. And the back cover came from hard2find accessories (via Amazon). I wrote them, and they sent me a new cover. And it works! FINALLY. It all works.
Try getting a wireless charging cover. And if that doesn't work, it might be time to replace the phone.