iPod Touch 4 stopped indicating charging from wall (or updating Apps)

Last week my daughter's iPod Touch 4 stopped indicating it's charging when plugged into wall-- no bleep noise or bolt sign on battery that it's charging. But, it doesn't lose charge completely and die either. The battery meter just freezes. But, when I plug it into my Macbook it charge (bleeps and bolt sign both happen) and it's recognized in iTunes. It's not the cable-- I tried several cables without success, yet those same cables charge my iPhone 4s no problem from wall. The same cables are what charge it with my Macbook... so definitely not the cables.

I recently upgraded her iPod to iOS 6... not sure if that has anything to do with it. Also, it won't update apps at all... not even when plugged into iTunes and charging. I have to update them in the Apps section in iTunes and then sync it. Very strange.

Is it the battery that's going bad? The iPod is 2 years old and gets daily use.

Thanks in advance for any help!