1984 Nissan 300ZX Brothers Having Fun

Electrical problem
1984 Nissan 300ZX Automatic 110000 miles

We have a 1984 Nissan 300zx that my younger brothers drive around. WAS a very fun car, but they tend to neglect it from time to time, so it gets its fair share of a beating.

Last week they drove it to school and decided to leave the head lights on. Needless to say, they needed a jump at the end of the day. One of their friends had cables and helped jump the car. When they jumped the car they crossed the cables (That's right. Negative to Postive and Postive to negative.) They let it sit for a little while, then the battery started smoking on the Z. After sending smoke signals alerting them of their error, they switched the cables so they were then properly affixed. The car ended up starting, but running really rough. My younger brother drove the car home and said, "It is only going 35 miles and hour with it pinned."

So. I am trying to figure out what might be wrong with the car that it is now running rough at idle. I have replaced what looked like a fuse wire for the battery that was attached to a plug, and I am having the battery tested today to see if it can still hold a charge.

My questions is, what else should I be looking for while trying to get the car back to tip top.

Thanks,

Andrew