Thanks.

Based on the information you have provided, it is most likely that you are experiencing a failure of the water-shut valve motor on the center of the AC box.

On typical HVAC systems you have a heater core inside that generates heat and an evaporator core that generates cold, and air is aimed over which one you request to supply the desired air temperature.
On the 2002-2003 Galant this system is slightly different. Because of the amount of radiant heat that is generated from the heater core, it has a supplementary step to insure that the AC is still working at peak performance regardless of the excess radiant heat. This consists of a valve just ahead of the heater core which is used to shut off the flow of coolant through the heater core. By cutting off the flow of coolant through the heater core, it prevents the core from generating that excess radiant heat except for when it is needed by setting the heat dial.

Now getting back to your problem, the water shut off valve is controlled by a small electric motor which opens and shuts the valve based on your requests from the temperature knob. These motors are well known for failure; the symptoms when they fail are either no heat whatsoever, or insufficient cooling (if it fails with the valve open instead of closed), accompanied by clicking noises from the motor as the gear strips out when you turn the temperature knob to extremes, making it try to move the valve.

Based on your initial symptoms as well as the additional information you were able to provide, it sounds pretty certain the water shut off valve motor has failed (not the valve itself, the motor).
A new motor will run you about $140 from Mitsubishi. Installation takes about one hour, and can be done without dash removal. You can get to the motor by removing the radio/ac controls as well as glove box to gain access. Expect about one hour in labor to have this replaced for you.

If you have any questions, just let me know; I would be happy to elaborate.Doug C41026.0846362616