No air conditioning after a water pump and timing belt change

I took my car to a mechanic to have the water pump and timing belt replaced. Everything was working really good, air conditioner, radio and engine.
When I went to pick it up, everything seemed to working okay until I tried to turn on the air conditioner, it would not turn on. When I checked to see what the problem could be I notice that there was a wire from the air conditioner compressor that was disconnected. I took the car back and told him the problem.
After a day, he told me that the computer was shorted out?
My question is, if the computer was shorted out, wouldn't the car stop running? He told me only the air conditioner part of the computer was out?
What is your opinion on this matter?