Ok. So I got an 86 T/A from Washington. I had it barged up to my little island in Alaska I call home. When They went to drive it off the barge the battery was dead. They got it jumpped and left it idleing to let it charge. After some time idleing they saw smoke coming from the engine compartment and popped the hood to find a relay on the drives side firewall on melted. The battery still wont hold a charge, and the passenger side headlight wont raise up (If I rase it manually its fine and will even close by its self). Why did the Relay melt? Will it happen again? Will replacing it fix my headlight problem? What is the deal with the battery? Please any help is much needed.

Thanks