What is indicated by a battery warning light in a dodge neon?

Probably that the alternator is not functioning to charge the battery for you. Have the charging system checked out for you. Check to see if the battery terminals are clean. A simple eye inspection is not always enough. Batteries accumulate corrosive sulfate between the hold-down clamps and the battery terminals that you don't see, which can block the recharge energy from the alternator to reach the battery for recharge, thus, turning on the battery light. Unscrew the negative cable first and submerge in water mixed with bicarbonate and wash using a brush.