Old schooler needs new school help?

Ok, Mother mother got a hold of me and told me her car wouldn’t start. I went to check it out. No power to anything. Went to check the cables and they were putting off heat. Told her that it was an electrical problem. She said to get a new battery, which I new wasn’t the problem. But I got the battery any way because she insisted. Went to install the battery and sparks started flying and smoke poured out and lots of heat off the terminals. Im am very handy with mechanical but my knowledge of the electrical components is limited with these newer vehicles. Give me a carburetted engine with a distributor any day. So, any way, it is a 94 buick skylark with a 3.0. Any one know what component may be at fault. Cause all I can come up with is the electric management control off the top of my head. This buick has been plagued with electrical problems and I have so far held my own in keeping it up and running for her, even though I am not an electrician. Any help is appreciated.

sussex electrical