It seems there are variations of this issue for some folks. Some have issues with the chargers, some batteries, and some the actual phone.
I've been dealing with this for a while (check page 1 and 2 of this thread) and here is a list detailing my issues and what I've tried.
1.) Phone worked and charged perfectly until the first time I let the battery get so low that the phone shut off. Would not charge at all after that. USB connection worked, but no charging at all. Tried every variation possible with different outlets, a 1 amp charger, the factory 2 amp charger, a 2.1 amp charger, 3 different computers, and 3 different USB cables, all known to work on other devices. None worked. Solution - factory reset fixed it.
2.) Same as #1 above, but this time the factory reset did NOT work. I started charging my battery on an external separate charger and even bought a spare battery to have one in the phone and one charging at all times. Issue present with both batteries. Deletion of battery stats file has no effect. Solution - none known at this time.
3.) If your battery is in the phone and even slightly charged, you can power the phone off and leave the USB cable plugged in and the phone will vibrate every 5 seconds or so. I *think* this is the phone trying to charge but it is not able to do it. The green battery charging screen does not come up any longer either. I charged one of my batteries to 100%, put it in the phone but did not power it on and just left it with the USB cable plugged in so it did the 5 sec vibration thing just to see what the outcome would be. In less than 2 hrs it completely killed the charge of the battery and the phone (and battery) got super hot. I let it cool down, swapped to another fully charged battery and booted up the phone. Now USB doesn't work at all! No recognition that you have plugged in a USB cable by the device! If you power the phone off and have the USB cable plugged in, it will still do the 5 sec vibration thing so it DOES recognize the USB cable with the phone off, but not when it's on anymore. I don't see anything in logcat indicating issues with USB or that it even notices that a cable has been plugged in or disconnected. Changing settings in build.prop have not helped it recognize the USB anymore even though I try to force it to mount various ways. It's as if the USB port or firmware are inoperable, but remember - it still "works" if you power the phone off and have the USB plugged in because it will do the 5 sec vibration thing until the battery dies. Solution - none known at this time.
I really don't know what else to do at this point except turn the phone in for a warranty replacement. If anyone has ideas of anything else I can try, please let me know and I'll fill you in on the results.