AC Compressor - Can't Start My Car

What is your question?

My car was having trouble starting. But, it'd run fine once it got going. Then, my AC suddenly started shooting out humid air. And, within 2-3 days, the car would not start at all. I had to get it towed to the shop. They're telling me it's the AC compressor. But, wouldn't the AC compressor just affect my air conditioner? Or would a broken compressor cause my car to stop running? Thanks for the reply!