[ImperialCrown]

The 5-prong cube relay is standardized and should be the same pin-out. You should see the terminal numbers molded into the plastic. There are a couple of different physical sizes and current ratings.

5-pin-relay.gif

The dash HVAC controls and rear wiper may be failing. There is a way to calibrate and diagnose the HVAC in Alternative #1, 2 or 3 here:
http://www.allpar.com/fix/codes-climate.html

 

[ImperialCrown]

I think that the 23 in the odometer would be a PCM fault code and not a HVAC fault code. 23 looks like the Intake or Ambient temperature sensor.
You might try a battery disconnect to reset the HVAC control, but the control itself may be in trouble if it doesn't run diagnostics.
The Blend door swings between warm or cold air or a 'blend' of both. If you are able to get the temperature that you want, the blend door actuator should be OK.
The panel/defrost selection is controlled by the Mode door actuator or HVAC control.

 

[ImperialCrown]

You are correct. If the connector is different, don't try to defeat the plastic key. It isn't meant to be plugged in on purpose.
I don't know if a scan tool that can communicate with the BCM or HVAC module will help you here, but it's either that or finding another 2000 minivan dash HVAC control to plug in for a test.

 

[ImperialCrown]

The cooldown test measures the difference (temperature drop) in the evaporator temp from when starting out until after about one minute of cooling.
Before the test it may be good to warm the evaporator up by blowing heated air through it in the heat mode before running the cooldown test. This will assure a larger temperature drop and a passing test. Starting out with a cold evaporator will cause a failed cooldown test.