The MODE selection flap(s) is not working. It directs airflow from the blower to the windshield, dash vents, or floor depending on how it is moved. If you remove the glove box(maybe door too, some will open further than others0, and look inside you'll see the heater plenum. Depending on year, you'll have a cable & lever that move the flap or, likely in your case, a 'stepper motor' that is attached to the pin on the end of the 'hinge' that the mode flap rotates about. The stepper motor can break the pin, and it will go zzzt zzzt as you change mode, but it won't move the flap, or the motor itself could fail, or the control switch. Have you checked fuses? Does it make any noise when you change mode? If you turn the key to ON, and sweep the mode through its arc, you may hear the motor try to move if you get your head near enough to the 'works' via the glove box opening.
One other style uses vacuum 'motors' (diaphragm with pull /push rod attached) that move the flaps around. In that case the control has a 'maze' to connect the this-thats at the proper time for the mode you select. One key factor is that loss of vacuum or control will default the mode to defrost for safety in winter(you can drive w/o A/C but frost on the windshield is not a good thing.) THe maze will connect flaps to direct the air appropriately. If the vacuum source is compromised(cut hose, loose fitting under dash or under hood) it will default to defrost. The 'motors' look like small cans with a shaft sticking out one end and you can generally see them through the same glove box opening.
tom