Sounds like what I had recently.
It started by simply smoking out the USB connector when I plugged the phone in to charge, then it displayed similar symptoms: did not accept charge from the wall wart, the USB-cable worked, but no data transfer was possible. It did show as charging, but the charge animation continued even when I unplugged the phone from the USB, so I assumed it was bogus.
When turned off, it reacted to the AC charger similarly: battery displayed, then the displayed stayed on when I unplugged it.
The repair shop accepted it under warranty, and fixed it, but the repair slip was left unfilled, so I'll never know what they actually did and what the diagnosis was. All I know is that the motherboard was not swapped out, as I retained all my data.
Google Nexus S I9023