The most common cause of a melted ground wire is when a battery has been connected backwards, with a large current flowing through the rectifier. Since the rectifier is connected to the battery directly, if damaged it can drain the battery even when the key is off. See if the wires have any evidence of overheating.
Make sure the battery is disconnected before you try to charge it, and most tenders are not proper chargers. Even some "smart" chargers won't start to charge if the battery voltage is too low.