I only have passing experience with the digital display HVAC controller. It's CPU is buried inside the HVAC head in the dash.
Remove the control head from the dash, remove the knobs from the encoder shafts, Remove the through screws that hold the face in place, and separate the face from the back 2/3 of the HVAC controller case.
There were two circuit boards inside my HVAC controller.
Directly behind the face is the digital display/encoder circuit board with a high density wire connector plug wired deeper inside to the actual CPU board. The display/encoder board is the only one I've removed from the housing since I was replacing the burnt out panel illumination bulbs.
It's pretty obvious how the display/encoder board comes out of the rear housing. The white plastic housing is likely fairly brittle and the board is super thin in comparison to a standard thickness PC board so treat it with care.
I was only interested in the display/encoder board so I didn't pay a lot of attention to the CPU board and how it was attached to the housing.
If the CPU board in the back of the housing is as thin as the display/encoder board you'll need to be very careful with it. I don't remember any noticeable large diameter connector pins on that board so with luck it's not soldered in place to the connector molded into the HVAC control head like the 4wd switch bulb board. I had to drill out some 2mm Hakko desoldering tips to around 2.8mm remove that 4x4 switch bulb board from the housing.
If they melted plastic posts to fix the CPU board in place it could be miserable to liberate it from the housing.
Once you're sure you have the controller working again... It might be good to replace the tungsten display bulbs so you don't have to monkey with it again. My bulb bases turned to powder as soon as I touched them. If the new bulbs don't have them it's not the end of the world. My replacement bulbs had bases but the wrong color silicone caps. I transferred the original blue silicone bulb covers to the new bulbs so the lamp color doesn't stick out like a sore thumb.
Here's the Bill Herd and Adrian Black video I referenced where Bill is talking about the difference between consumer chips vs industrial chips and industrial vs consumer board design and how long stuff was designed to last back at the dawn of the consumer electronics age in the late 70's.