There are a few things that could be checked. Firstly, if you can, replace the battery, it may be unable to hold a charge. The second potential problem is that the connectors from the battery to the motherboard are fried, that's a bit harder to fix and will either require a microscope and dam good soldering or replacing the motherboard.
Your problem likely falls with the headphones. Try them on someone else's phone or computer and if they don't work then you will need to contact whoever sold them to you to get them replaced or to get a refund. Other people have had this issue: http://www.samsung.com/ca/consumer/mobil...-phones/tablet-accessories/EHS44ASSBEBSTD-reviews/consumer-reviews?subsubtype=others-multimedia