How does the passenger side dash come out

many cars automatically kick on the air compressor in defrost, to dehumidify the cabin air

On a 1996 model you probably have vac actuators that control air flow. Look under the dash and you may be able to see the actuator that controls flow to the defrost and vents. There would be another one for temp control.

Mode Door 1.
a.This door regulates air flow to either the dash vents or defrost/floor. If you have air flowing only through the vents with no defrost or floor, this door is failing. From our experience, this door is usually the first domino to fail. Not sure why, just is.
<!--[if !supportLists]-->4.Mode Door 2.
a.When mode door 1 is set to divert air away from the vents and into the second stage of the system, door #2 chooses whether air goes to the defrost vents to the windshield or out through the floor vents in the passenger and driver's side footwells. Failure is indicated by an inability to choose between defrost and floor.
b.This door turns out to be the most difficult to replace. In order to replace the door, the dash panel has to be removed. It's still better than the dealer fix because you don't have to evacuate the AC system, drain the radiator, and remove the plenum box. But it is more work than the other fixes. When this door breaks, it falls in the down position, blocking the floor vents and diverting all air through the defrost vents. From a safety standpoint, this is good since you'd most likely rather have a clear windshield than warm feet. We suspect that a large percentage of customers will just leave this door unrepaired. You will have heat through the dash vents and to the windshield, just nothing to the floor. It's inconvenient, but you'll have to make the determination if warm feet are worth the extra work to fix the door. An extra pair of socks is easier.

You have a air box heater box air divert valve stuck you will need to replace it first start by looking under the dash passenger side you will see a round part with some vacuum hoses coming off from them start engine switch your location function switch see if working on divert er vacuum you most likely will have to replace your divert er valve.

You have a vacuum leak or the little valve in the vac line on the passenger side of the intake is bad

One of the Actuators for the doors inside your dash that controls and diverts air might not be working correctly. You may have to either replace the Actuator or Replace the A/C Heater Control. Your vehicle does not come with a Cabin Air Filter.

your mode door sounds like it is not moving
the air distribution is control by an actuator(motor) that sits on top off a door that moves to distribute air flow to whichever setting you set it to-if the door is broken it will no longer move and will stay on one setting all the time-the same thing will happen if the motor is no longer working. the only way to be sure is to physically check the motor. this is located on your heater box which is the large black box that is under the dash on the passenger side(it very big-just look under the passenger side dash and you will see it)if the motor is not working-replace it-if it is working you will have to replace the whole heater box which can be a pain-usually the dash has to be removed.
hope this helps

Instrument panel upper trim panel


Instrument panel

1. Disconnect the negative battery cable.
   
2. Disable the Supplemental Inflatable Restraint (SIR) system.
   
3. Carefully pry upward, using a small, flat-bladed tool, to remove the defroster grille.
   
4. Remove the Sunload and Headlamp Auto Control sensors from the defroster grille.
   
5. Working through the defroster grille opening, remove 3 upper trim panel retaining screws.
   
6. Remove the heater/air conditioning vents from the front of the instrument panel by releasing the tab on each side from inside the vent and pulling out.
   
7. Working through the vent openings, remove 4 upper trim panel retaining screws and remove the upper trim panel.
   
8. Remove the instrument cluster.
   
9. Remove the right and left A/C vent trim panels.
   
10. Open the trap door in the rear of the glove compartment and remove the passenger inflatable restraint wiring connector from the retaining clip on the rear of the glove compartment assembly.
    
11. Remove the 4 glove compartment-to-instrument panel retaining screws.
    
12. Pull the glove compartment assembly outward enough to access the wiring connectors for the glove compartment switches. Label and detach the wiring connectors.
    
13. Remove the glove compartment assembly from the instrument panel.
    
14. Remove the retaining screws and courtesy lamps from the right and left sound insulators and remove the sound insulators.
    
15. Remove the steering column opening filler trim by grasping at the front and rear edges and pulling downward.
    
16. Remove the 4 retaining bolts and the steering column opening bracket.
    
17. If equipped with full console, remove the console.
    
18. If equipped with mini console, remove the radio.
    
19. Remove the headlamp switch module.
    
20. Remove the 2 bolts and the hood latch release.
    
21. Move the driver's seat to its full rearward position.
    
22. Remove the steering column.
    
23. Remove the 8 instrument panel retaining screws, detach the wiring connector at each side of the instrument panel, and remove the shims at the lower mounting screws.
    
24. Remove the instrument panel with the aid of an assistant.
    

To install:

1. With the aid of an assistant, position the instrument panel in the vehicle.
   
2. Attach the wiring connector at each side of the instrument panel, install the shims and the 8 instrument panel retaining screws.
   
3. Install the steering column.
   
4. Install the hood latch release with the 2 bolts.
   
5. Install the headlamp switch module.
   
6. If equipped with mini console, install the radio.
   
7. If equipped, install the console.
   
8. Install the steering column opening bracket and the steering column opening filler trim.
   
9. Install the right and left sound insulators.
   
10. Position the glove compartment assembly and attach the wiring connectors to the switches.
    
11. Push the glove compartment into place and install the retaining screws.
    
12. Place the passenger inflatable restraint wiring connector on the retaining clip on the rear of the glove compartment assembly and close the trap door.
    
13. Install the right and left A/C vent trim panels.
    
14. Install the instrument cluster.
    
15. Position the upper trim panel on top of the instrument panel, making sure the sensors are through the trim panel.
    
16. Install the upper trim panel retaining screws through the heater/air conditioning vent openings.
    
17. Gently push the heater/air conditioning vents into place.
    
18. Install the upper trim panel retaining screws through the defroster grille opening.
    
19. Install the Sunload and Headlamp Auto Control sensors to the defroster grille.
    
20. Gently push the defroster grille into place.
    
21. Enable the SIR system.
    
22. Connect the negative battery cable.
    

Had the same problem. believe it or not i changed the gas cap and got heat all around. something about pressure.

Have you checked the diverter doors under the dash??
It sounds like a vaccum hose may have fallen off your vent controller.
I have had similar problems and found that the air WAS moving, but it was all going up through the defrost vents at the windshield.
A quick check of the vac. lines showed that one under the glove box was pulled off.
with the engine running, try setting the air settings to all the options ( vent/floor/defrost..etc..)
See it you can feel or hear the diverters moving under the dash..