Since the laptop seems to be working, except for the non-charging, I'm going to say that you shorted either the charging cicruit on the motherboard, or the battery charge control circuit.
If you know enough to see if the voltage is correct on the connector to the battery, I would suggest that you try that first, before you try a new battery.
I can't help any more than that, though, as I do not have a G-series laptop to look at to give you more details.