If radiator fan resistor is bad you have NO LOW FAN, only high, could easily be that or a relay. Pull the resistor connector at top of shroud and look for melting. Turn a/c on and if low fan doesn't come on then again resistor or low fan issue.
Problem should be easier to fix than other overheat issues.
Be very careful, you have no idea of if they have severely overheated it to yield headgasket at all. That can be done sitting at a stoplight.