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There are 2 control units for the HVAC system. The control head in the dash and a box (located under the dash on the driver's side) that switches the vacuum (vacuum is used to actuate the dampers that direct where the air goes) to the location that the control head is set to. Your problem could also be a simple as a break in a vacuum line.
My '96 CE has done the same thing for some time. It will still
switch to dash vents eventually but it's waiting longer and
longer to do it. I've read sraft's suggestions before since this
seems to be a regular problem for later model C4s. I looked
under the driver's side but like most other C4 projects finding
room to manuver hunting for this vacuum thingie is going to
be a PITA so I let it go for now. Guess I'll deal with it when
it quits switching completely.
Doors are controlled by vacuum based on electronic signals to one of 5 solenoids. Defrost only is the default and indicates there's no vacuum. Find the source in the engine compartment and then follow it to the check valve that keeps vacuum flowing in one direction only. Usually the check valve has broken - if you can blow air through in both directions, it's bad. Replacement is about 9 bucks.
When my '94 did the EXACT same thing, it was just a plastic vacuum check valve that had cracked, and was a $5 fix! It's located under the passenger side fuel rail cover, and i'll bet'cha a donut that it's cracked.
BUT...if you still need/want to change your A/C controler and programmer, i have one of each that i bought that i never installed.