I have a 2002 Town & Country with climate control and the blower runs on high whether or not theA/C system is on or not.
Does this sound like a bad blower resistor module?

 

Yes, sort of. If you have the automatic temperature control (where you set the temperature digitally), then you don't have a blower resistor but something called a "blower control module". It doesn't contain resistors-- it has electronics that receive digital commands from the control head and then quickly cycles the power on and off to control fan speed. I've had two of them die on my van-- one died with the fan on high (even if the climate control is turned off) and the other died with the fan off.

The main difference from your perspective is that it's a lot more expensive than a resistor block-- I paid about $70. Fortunately it's easy to replace though. Just open and empty the glove box, squeeze the sides together and let it hang down. You'll see two connectors going into the HVAC box-- take the connectors off, then use a phillips screwdriver to remove the two screws that hold the control module in place. Put the new one in and you're done.