Here is a quick run down of what happened.
Earlier this summer I replaced the battery. It was old and not holding a charge. I rode the bike maybe 2 or 3 times in the next few weeks. On the last ride, it started misfiring past half throttle on the way home. I parked the bike and didn't touch it for a few weeks. I went to start it again and it was dead. This is when I found the battery with the melted terminal. So i got a couple rides with it between changing the battery and the battery somehow draining.
To answer your questions:
Was the sparking with the damaged battery, or new?
And, was the key on or off?
Did you have the battery dropped out of the battery box before you attached the negative cable, or was it in its normal location?
Yes, I dropped the battery box. Really the only way to change the battery on these bikes.
I'm concerned that the positive cable has damage, and can short to the frame.
I pulled out the DMM. There is no continuity between positive battery terminal and frame. Nor is there between battery side of the solenoid and the frame. When I disconnect the hot cable from the starter, there is no continuity between the starter side of the solenoid and the frame. No fuses are blown. This is why I'm wondering if it was the battery that is defective. I assumed it was a short too but I can't seem to find anything indicating that. That's why I'm thinking it was a defective battery.
I'll thoroughly check the positive and negative cables again. Maybe even remove them and clean the terminals. Every google search I'm reading seems to point the cause of a melted terminal to dirty connections. I'm not convinced that's what caused mine but I'll give it a shot.
Any other ideas? I appreciate the help so far!