A general idea of how it works would be that any time the fan is running, you should have air coming out of the system from somewhere. Floor, dash vents or defroster vents. There are several doors inside the climate control box that direct the airflow to the selected discharge opening.
One is controlled by a cable that's attached to the temperature selector knob on the dash. The others are activated by small electric servo motors. Those motors are controlled by the various push buttons on the climate control center. I suspect that you might have a problem with the circuit board on the back of the climate control panel if your fan blower motor is operational.
Doing an engine swap or removing the AC components shouldn't affect the air flow coming from the system. I think they're unrelated.
You did not mention the year. I have an 88 GT. A few years back I had the same problem This is what worked for me. On the pass. side , toward the front of the consol there is a space before the duct work. If you look with a flash light, you will see a rectangular box approx.4or5 inches long with a wiring connector attached. it is bolted to the duct. FRom the pass. side with a screw driver,turn the key to on {not started} , turn the fan to the med position. Now press the vent button and listen for the little motor to start. if nothing happens tap that little box and see if you get any results. Still nothing?? press the off button and listen. What happens is the crud that has accumulated over the years has made it more difficult for the motor to go all the way to the correct position. If you keep trying the buttons one at a time you may free it up. always go to the off position and listen for the motor before going to the next button. If you have patience and the right tools you can clean everything up. if you try that approach you'll find that connecting the motor to the duct door is a real muzzer. Good luck
