Is it the petcock in the radiator? If it is a plastic screw type I normally heat a screw driver with a propane torch and stick it firmly into the broken petcock. The screw driver melts the plastic and as it cools down in a few seconds the plastic solidifies and you can just turn the screw driver and remove the broken off pet cock. Could take a 20 minutes to half hour, or worse case the radiator could need to be removed. I suspect you will be charged between half an hour to one hour unless it is suggested to drain/flush the cooling system.