A/C Compressor went out

First off, I had my car checked out and the A/C compressor is not functioning. The A/C would sporadically cut out, not often at first only once or twice a week, until finally a couple weeks after the A/C now will typically not work at all. I realized this was after I jumped a Nissan Altima 2005. I jumped this car about 4 or 5 times before we were able to replace the battery. I also found out we did not jump the car accurately. We had positive to positive and negative to negative. I know I read it can mess up the Alternator or ECU, but my question is, is it possible that jumping this car messed up my A/C compressor? I have not had problems with my A/C compressor before on my last two toyotas and I drove both of them until around 130,000 miles.