Plugged in my G2 overnight Saturday night when it was down to about 25%, woke up on Sunday morning to see it hovering at around 80/81% and discharging. After looking at the battery stats, I was able to tell that it charged to over 90% before stopping charging completely and starting to discharge.
I was using the original cord and power brick when it happened, if that makes any difference.
I have confirmed that the issue is not any of the specific chargers that I have around (either the cords or the brick, and have used both the OEM one as well as others) - and I have booted into Safe Mode to see if that would solve the problem - it did not.
Luckily, I was able to get a wireless Qi charger from a friend as that is the only way that my phone will (very slowly) charge.