Q: How can I prove my car dealer's service department broke the CD in my Hyundai Santa Fe?

Last week, I brought our car into the Hyundai Dealer's Service Dept. The AC was not cooling air properly on the drivers side (passenger side was fine). They performed some diagnostics... actuators working ok, said heater box needed to be replaced. We plan to get a 2nd opinion, but when we got the car back, the Infinity CD player would not work. It said "Initializing", but would not do anything. The service tech said they were working under the dash doing the air conditioner diagnostics, so told us to bring it back in. He sent us to a audio store, who said that it would need to be replaced. We are sure that something happened to the CD player while it was in the shop, but car dealer is saying we they can't be sure they caused it, and that it could have already been broken, thus they say we need to pay for the repair/replacement. I know the CD player worked before I took it in to the shop for the AC issue, as I used it just prior. Is there a way to prove they caused the issue?

My car has 105000 miles.
My car has an automatic transmission.