If the laptop runs okay from the A/C adapter with battery removed (try it), the adapter/charger is okay I would say.
If the battery level is continually falling (percentage never gets higher, always lower) I'd be more inclined to say the battery needs replacing . After a few years they can no longer hold a full charge, especially if it's attached (or has been attached) to a laptop which has been run from mains power for long periods. In such a situation the battery should have been removed & stored away until needed.
Another possibility, if the battery is okay, is that the charging circuit inside the laptop is faulty.