Dave,
Here's what I got out of the service manual:
To put it in diagnostic mode press and hold down the rear defroster button, then press and release the blower manual up button. If it's a convertible press the ext. temp then press and release the auto fan.
You will get a number 1 through 9 preceded by a minus sign. You advance through the modes by pressing the warmer button. Display the contents of any mode by pressing the cooler button. Here are the modes: 1 - program number, 2 - in-car thermistor, 3 - ambient correction, 4 - blower number, 5 - outside temperature thermistor, 6 - feedback pot position, 7 - calculated door position, 8 - system faults, and 9 - software version number.
So you will want to get to mode 8 and display the specific condition. Here are the error numbers for mode 8: 00 - program number, 01 - feedback potentiometer open, 02 - ambient sensor open, 04 - ambient sensor shorted, 08 - in-car sensor open, 16 - in-car sensor shorted.
It then has about 15 pages of diagnostics tests to perform depending on what error number you get. It's pretty involved, grounding certain wires to isolate the problem.
For what it's worth I had problems with my climate control and ended up replacing the whole unit. You will find procedures for cleaning up the connections on the back of it. I tried it a couple of time so I ended up biting the bullet and get getting a new unit. That was probably 10 years ago and no problems since.
Hopefully this will help. There are a lot more folks here who are way more knowledgeable than me so if this doesn't help you may try sending a pm to GMJunkie who is pretty knowledgeable about all Corvettes.
Ron
"Baldie88"