2007 Ford 500 SEL Interior fan

When the car is started, and the HVAC system is off, everything is fine.  As
soon as any setting is touched (either AUTO button, or any of the preset
position buttons, or even the fan speed button), the fan runs on high, and will
not shut off until of system off button is pressed (below the AUTO button) and
the car is turned off.
The resistor has 5 blades (4-pin connector), most of the parts stores around
have a 4-blade, 4-pin replacement that is supposed to work with this model’s
Auto function, but when I replaced it, and try to turn on any setting, nothing
happens.  When I put the old resistor back in, it reverts:  once any button is
pushed, it stays on high until the vehicle is turned off.
Two more things to mention:
- when I put a meter across all combination of pins on the new one, I could
not get any resistance readings, while on the old one, I only got (1) resistance
reading of .4 ohms across (2) pins, but nothing across any others in any
combination.
- I got 12VDC when I measured the pins on the harness, but could not see
different outputs when I had the harness unplugged, and was changing the
speed of the fan (based on the speed control display on the console).

I am not sure if there is a speed switch for this model, but if it were a faulty
speed switch, wouldn’t the symptoms have been the same with a new
resistor, if the speed switch has a bypass wire for high that goes right to the
blower motor wiring from the battery?

Any guidance is appreciated -