What can be damaged by hooking jumper cables up the wrong way?

My car battery was dead so we asked someone for a jump and when we tried starting the car, the negative jumper cable on my car started smoking. We brought the car into the shop and he said someone must have hooked the jumpers up wrong and that i needed a new battery. When I went to get my car, with the new battery, the car would start and run just fine; but the vent was blowing full blast and the radio/ac panel wasn't lit up and none of the buttons would work, and I also found that the odometer and speedometer weren't working. Are these all controlled by the same computer? I was wondering if it sounds like damaged wiring, fuses, a computer, or something else. Could anything else be damaged in my car that's not immediately apparent?