So your Verizon Galaxy Nexus won't charge, charges sometimes, or thinks it's charging when it's not plugged in? It might be time to replace the micro USB connector board.

For this repair you'll need:

An opening tool.

Small Phillips screwdriver.

A replacement micro USB board. I found mine here.

The original board I removed was revision LF-A G 1145. The new one (pictured) was LF-A G 1150 23-3.