Dear FireBird Stud. My 94 Lesabre did exactly the same thing. I have flushed the heater core, changed thermostat, and replaced the heater control assembly. Just changed the heater control today, found one at junk yard for $20. When you stated you can push the rod, that tells me, and should also tell you the servo motor has stripped out gears. Now if you pushed it hard you may have stripped them out, but I doubt it. After I changed my control unit I went to the heater door and found the servo unit. Removed it from the heater housing and I am now attempting to determine if it is bad. There is no way you can push that rod and spin that little DC motor without breaking something. I have juice to the servo, three wires in, one is hot the other two probally run back to the controller or the programmer. I am headed back to junk yard to rob that Lesabre of the servo unit and the programmer which I can easilyh get at from the glove box removed. Don't know bout your car. Odds are it is that servo cause you can move the arm. I dismantled mine and there are 5 gears in it and 4 of them are reduction gears, no way will you spin that motor by pushing that rod. Good luck are you in the twin cities, if you are, call me and I can tell you where you might find some cheap parts.
Phone number deleted,
I would suggest not posting your phone number in the open area of the forum, you can PM him or list the places you are talking about