It sounds like your battery cells are dead, therefore they will not charge. Since your laptop is only 6 months old, the battery could be dead due to leaving the system in hibernation mode for extended periods, or not discharging the battery fully before recharging repeatedly.
It could also elude to an issue with the power adapter/charger. Is it the original charger? It could just be faulty and not providing enough current to charge the battery. Although I would suspect the battery if your laptop is functioning with the power adapter plugged in.
You will probably have to invest in a new battery. You should ensure to get an OEM (Official Equipment Manufacturer) battery for your laptop make/model and not a cheaper non-OEM one, because...