Ford: all air conditioning, no heat, ford tauraus, core lines

Question
My sister has a 98 Ford Tauraus.The air conditioning  won't turn off unless its on vent. My husband put in a new radiator, thermostat, and flushed out the heater core lines and whatever else he thought needed flushed. He put in the prestone 50/50 antifreeze in the new radiator.  Unfortunately, it did not help with the no heat problem at all. Thats when they discovered the air conditioning was continuing to run and would only shut off on vent.  He's an auto body man and know more about old cars. He said he has no clue and neither did the guy helping him. If you have any suggestions we would greatly appreciate it.
Thanks,
Beverly

Answer
Hello

The airconditioning should only run on defrost, partial defrost, A/C, and max A/C.

If the compressor is switching on at other positions, you have a stuck relay, crossed wire, bad controller, or failed switch.

You will have to back track the wiring to see where the problem lies.

As for the heat.  With the A/C compressor unplugged, do you get heat?

Are the hoses to and from the heater hot when the engine is at temperature?

Does the airflow switch correctly as commanded?