Verified answer

Make and model would help significantly. It could be any number of things, from a simple relay to a more complex problem.

I would start by checking the fuses, there are also some relays that switch on and off the compressor. I'm guessing that you just have a blown fuse under your dash. Does the blower motor turn? If so than it is just the a/c fuse and not the heater fuse. Hope this helps.

You could tell us what year and make your car is to begin with.....someone here may know of a common problem.

Not much you can do yourself at this point. Take it to the shop and let them fix it.

Take it to someone that specializes in electrical. (dealer)