I have had this kind of problem too where my charger is fully OK and the battery works too. Even though the battery last for just 30 mins max. The recieving point of the charger does not accept taking in electricity to the G4 PB. I tried to open up the keyboard cover in order to clean the reciever. The charging process takes alot of warmth and makes the metal in the recieving part on the computer a bit dirty. In kinds of makes a layer of dirt/flame/electrisity-burn on and this layer is making it difficult for the elerctrisity to come through. I cleaned it up yesterday and the charger worked ok for a while. But the same thing happened again this morning and I tried to use a spray soap bottle and a toothpin to clean it again but it didnt work. Probably because of the soap and water still keeping it wet. You should wait until it get dried.
But what other options is there to solve this problem?