After you indentify any issue at the time to charge the item, the easiest way to verify if the issue is related to the battery or the charger is pluging the AC charger into the unit and wait about 30 minutes.

If the charger is warm to the touch, the charger is moving current to the unit, then the battery would need to be replaced, but if the charger temperature hasn't changed, the charger would need to be replaced.