The battery light can stay on for a couple of different reasons. Assuming your new battery is good (which may not be true and should be checked if all else fails) then most likely problem would be the alternator (generator in old Beetles). The light will stay on if the charging system is malfunctioning or the batteryhas completely failed, a bad battery itself may not light the light.If you don't have any test equipment then a professionals help will be required.
Have the output of your alternator checked,it should put out 14.5 volt. Also check the battery connection to virify that they are clean.
The alternator may not be recharging the battery .
Because the ignition is powered directly from the battery. The Gen/Alt only feeds the battery.
Defective alternator.
The battery light comes on when the alternator is not charging. Changing the battery did nothing. Either put a gauge on the battery to see if it is charging, or while running, disconnet the positive cable from the battery. If the car dies that means the alternator is not charging. Most parts stores will check it for free. Oriely's , Autozone, etc.
The battery light stays on when the alternator is over or under charging.
so you can see the battery after dark!
Your battery might be bad, or so might the alternator, or both. A bad alternator will ruin a good battery over time, and vice versa.
That light doesn't mean that your battery needs to be replaced. It means that your battery is not being charged while the car is running. Have your alternator tested.
check the alternator fuse on the main cable that goes from the alternator to the battery. sometimes the alternator shorts out this fuse. it's usually mounted on the right side of the firewall in a plastic cover over .
Your battery is not charging due to a problem with the battery cables or a bad alternator.
Likely the battery or alternator, but probably the alternator