I am gonna go out on a limb and say you have a wire problem. A bad battery new right out of the box is possible but not common. Having a failed charging system roast some wires when I shits the bed is pretty standard.
Start by retracing your steps and go over each wire and connector. You are looking for burnt connectors and wire. Pay attention to areas where the wire touches the frame. An over heated wire may have melted the insulation enough to be providing a weak ground that is bleeding off current.