If your wiring is hot you must have a dead short somewhere. As it won't go it could be the solenoid which engages the gearbox. If the motor starts with the starter you now have then I wouldn't put out the money for a new one until the other problem is solved.
Okay, lets think about this for a minute. If your battery is getting hot enough to boil, then it is getting too much juice to it. So, ask yourself this question. What generates the voltage to the battery?
If the motor is starting, as you say it is, then it isn't the starter.
If the positive and negative on the battery were crossed, then it would have most likely have blown a fuse and possibly the starter, ignition switch, and starter relay,(if it has one) would have fried due to the reversal of polarity.
