AC blows hot when ICE is running

Been searching the internet for days and have found similar post but no real answers.
My 12V battery died. I replaced it and back in business except for the AC. When the gas motor is running the air blows hot. When parked and the ICE turns off the air returns to cold.
I have checked the fuses and would not think it would be a freon or compressor issue when the AC works fine in electric mode. I am baffled at how a battery going dead would cause this kinda behaviour. Any suggestions would be greatly appreciated!