1969 Buick Electra 225 Starts TOO Well

Today I purchased a 1969 Buick Electra 225. It runs strong, but the problem I'm having with it is getting it started without catching the battery on fire or melting the cable. Right now, whenever the battery is connected, the beast roars to life, lack of key in the ignition be damned. Also, whenever the ground cable gets close to the battery terminal, we get lots of sparks that melt the terminal a bit.
The previous owner told me that he recently replaced the starter, which is when the problem started. We actually had to buy a new cable because the insulation on the old one had melted off. I've tried doing a little research on the problem, and the general consensus was that one of the wires connected to the starter might be out of place, but I've fiddled with it some and everything seems to be in place. Any suggestions would be greatly appreciated, I'm happy to provide additional details if necessary.
Thanks!
The previous owner told me that he recently replaced the starter, which is when the problem started. We actually had to buy a new cable because the insulation on the old one had melted off. I've tried doing a little research on the problem, and the general consensus was that one of the wires connected to the starter might be out of place, but I've fiddled with it some and everything seems to be in place. Any suggestions would be greatly appreciated, I'm happy to provide additional details if necessary.
Thanks!
0
Comments
Here are a couple pictures of the wire connections, I know they're not the greatest, the car isn't on stands yet and it's pretty late. I can take some more in the morning. Yes, I'm aware that one is disconnected, that's on purpose, we were fiddling while waiting for the tow truck and didn't have time to reconnect it. It was originally attached between one nut and the larger cable, closer to the starter.