Had to jump this vehicle since battery went dead

That's a GM product. They selfishly decided to stop allowing us to buy radio service manuals after 1994 so they could lock up all that repair business for themselves. Instead of paying the ridiculous repair costs, a lot of people installed high-quality aftermarket replacement radios. To combat that they cleverly designed the Body Computers into the radios starting with some 2002 models. Unfortunately you are tied to the dealership for this one, and their two grossly over-priced repair centers. Imagine, ... Designing a car that won't run without the radio. Who does that benefit?

All computers and radios have diodes in them that are supposed to protect them from reverse polarity. A diode is a one-way valve for electrical current. They are installed backward and do nothing under normal conditions. When the polarity is reversed, that allows current to flow through the diode just like a dead short. That causes the fuse to blow and protect the rest of the circuit.

Sometimes the high surge of current through that diode overheats it and shorts it. They may burn open causing the smoke you saw but typically they just short and cause new fuses to continue blowing. You might try to disassemble the radio and look for a two-terminal component that is burned. It will check shorted, like a piece of wire, with an ohm meter. A TV repairman can identify and measure them. The diode will be near the plugs on the back of the radio.

Keep in mind too that unlike people like me who troubleshoot down to the component level and replace just what's defective, the high-priced authorized repair centers just pop in a new circuit board. It takes less skill and less time, and they make more money that way. For that reason GM has never designed their radios to be easy to service. Most circuit boards are sealed and hard to unsolder parts from. Even taking voltage readings can be frustrating.

Diodes for this application are generic but most of the other parts that are likely to be damaged have to come from GM. They won't sell you those parts unless you supply the part number, and you can't get those without the service manual.