Try drawing/inhaling on the connection point of the battery without an atty/cart attached. If the LED lights, then the battery is still technically functional.
Be sure that the charger is functional and that the battery has charged fully. With the USB charger, wait until the light turns green and stays green for at least a 10 sec count or longer. With the PCC, be sure that the PCC is fully charged. Charge until the LED light on the side goes out for at least a 10 sec count.
If it isn't a charging issue, then my suggestion is return it and get another.