Check the cabin temp sensor first . Make sure it's drawing air and not clogged with dust.

Sounds like the PBU (push button unit) isn't happy. If it's a pre-86, it'll be easy to open the unit and check the solders. I have sparky friends do that for me. Post-85 are more complicated since they incorporate a controller that's external in the pre-86 PBUs. Post-85 PBUs are less likely to revive by reflowing solder.

Sixto
87 300D