Heater/air control switch

I think that your situation is like mine. You can hear the blower motor running, but no particular vent control. Your mode switch is probably air controlled.
Up underneath the dash on the passenger side there is 3 air actuator valves, and 1 of them is bad. I looked up under the dash with the car running and moved the mode switch to one position at time to see which one didn't move the linkage for the vents.
Today I replaced the one that has 2 air lines going to it, this one directs where the air flow should go, now mine works like it should. The part only cost me 30 some dollars from a gm dealer. It was a little difficult to change, due to lying upside down looking up under the dash. But I think before you go that far, check in the engine compartment, where the blower fan is in the firewall, there is an airline that draws air to operate the mode switch, see if there is suction there first, if not follow that line it may be collapsed or broken.