I have a 2004 ford taurus, the ac compressor does not work during defrost, but other wise works fine.

SOURCE: LOCATE AC CABIN AIR FILTER

no cabin filter on 2003 crown vic cabin filter is under pass cowl trim

SOURCE: ac repair procedure 2003 ford taurus

recover r134. remove cooling fan and shroud assembly. Remove surp belt. Unplug compressor connector. From under car. Remove ac manifold retaining bolt. Remove O2 sensor from exhaust for clearance. Unbolt compressor and remove (some of the bolts will have to be inserted into the new compressor prior to installation. Reverse all steps and evacuate and recharge system.

SOURCE: ford taurus ac stuck in defrost

Check under the hood for a vacuum leak near the firewall on the passenger side of the car. The blender door is vacuum operated and a leak would prevent the door from changing which vents the air blows. Hope this answers your problem. All the best!
Greg

SOURCE: My 2001 Ford Taurus A/C is not working. The

Check to see if you have power at the electrical connector on the compressor. If power is there, check the ground on that connector. If both are good, the compressor or it's clutch is bad. If no power is found at the compressor connector, check for power going into the low pressure switch (found on the accumulator). Often, if the A/C is left on when the system is low on Freon, this switch will turn on and off repeatedly and be ruined. If there is no power at the low pressure cut out switch, the problem is in the dash.
Charlie

SOURCE: ac not working on 2004 s430

If you have the hood up stand outside while someone activates your air off and on and see if the clutch on the compressor goes on and off while they activate the switch. If that isn't it the it could be improperly charged system or your climate control door that opens and closes for hot or air is not working properly and only stays on heat.