I have connected battery cables and jumper cables both ways with no difference either way (you can hook them up in either sequence, just not backwards, like pos to neg). The only thing that can cause melting battery cables and hugh sparks is either a very large electrical load is turned on or a large direct short that is not blowing a fuse. If either is happening, you can get the results you are describing, but it has to be a 1) large electrical load (over 30-40 amps) and has no fuse protection, and from your description of events, it could be an energized and locked up starter. You could try disconnecting the main power wire at the starter and see if the problem still exists, but I would not fool around with this one. If you do not understand auto electric or don't have the right troubleshooting tools, take it somewhere. This is how fires start, and corvette fires usually burn to the ground, as fiberglass is extremely hard and sometimes impossible to put out.