Melted battery terminal

My 1997 Cavalier started to smoke when I started it and when I attempted to shut it off, the engine continued to shake like it was still on. I disconnected the battery cable and it stopped but the negative terminal is melted and it sparks if I attempt to reconnect. Before that I had some problems with the positive battery cable and would sometimes have to wiggle it before the car would start. Someone mentioned it may be a bad solenoid? All / Any suggestions appreciated.

Yikes. The car diesels after you shut it off? Perhaps it's extremely high carbon deposits. You need to get a can of SeaFoam. Run it on a quarter tank of high octane gas.

haha, you don't have to run high octane in it, just open it up on the freeway, hold it right to the floor, tht'll get the carbon out

"No really officer. Some guy on the internet told me to."

lmao, just don't get caught