Welcome to Android Central! Moved to the Galaxy Ace forum, because that model number is the Galaxy Ace Duos, not a Galaxy Tab. Or did you mistype the model number?
How do you know it's charging, if there's no actual screen indicator? Are you relying on the LED light? And even if the device says the battery is charging, this doesn't necessarily mean that the battery is charging up properly (or holding the charge). It would still be a good idea to try a different battery.