2013 A/c not working after radiator replacement - computer problem or getting ripped off?

My husband just got a new to us 2013 Malibu. After owning it for less than a week it overheated. We took it to a mechanic and were told it had a cracked radiator. We have only lived in this town/state for a month so we don't know much about this mechanic other than they were recommended by someone we trust & their reviews online. We paid to have the radiator replaced ($1200! With a 2 yr warranty) and when my husband picked it up, the a/c was no longer working (worked great before). Took it back to the mechanic where they connected it to their computer. When they manually told the computer to blow cold air, the car blew cold air. As soon as the computer was removed, it went back to hot air. The mechanic then tells us we need to purchase a new part for $120 from the dealer and "sometimes these things just happen." I'm having a really hard time believing the timing is just a coincidence but having no car knowledge, I'd like to get someone else's opinion. Are we being ripped off? Did they forget to reconnect something somewhere?