|Don't assume the new battery is good. Not sure how the charger determines when the battery is fully charged but it could be simply shutting off because of elapsed time. Your manual may provide some help.|
You may wish to look at the contacts from the laptop to the battery. If one or more are corroded or bent that could explain your issue.
Is the battery an aftermarket unit or an OEM replacement? Same goes for the charger.
Is it possible there is a setting that ignores the battery if enabled?