OK, so I also have a 2003 Galant. Success!
In case you can't find the DLC, it's right above the gas pedal, on the underside of the dash.
It looks like this.
(IMG:
http://www.ross-tech.com/vag-com/images/DLC_Pinout.gif)
Misc notes as I followed Hansel's procedure:
I also found that (for my car atleast) key had to be on the ON position.
I pressed the hazard button 6 times, which is equiv to turning it on and off 3 times.
It has to be done in rapid succession...>10 seconds. Also, on the first try I realized I had my paperclip in the wrong slots of the DLC, so use the diagram and help above in determining positions 1 and 4. My DLC was upside from these diagrams, so actually the bottom right position was 1.
Also, I replaced the battery before trying to activate the clicker...If you can't get anything to work, replace the battery on the clicker.
Hope this helps! I am so happy to be $50 richer and have a working clicker! Thanks everyone!!