I bought the same one from ebay.
Do you have a multimeter? Set it to resistance and put one wire on the middle pin and the other on one of the outer. Push the stick in one direction and thats the lowest value of the pot, the other direction the highest value. Mine had a 50k ohm potentiometer, so I assume thats what yours have. I was going to use a gc stick instead for my first portable. I hooked it up but it felt like it didnt give me full range so I ended up using the normal stick. Now am I in the process of making my second portable and was going to use the same controller again and decided to give my gc stick a second try and it kind of worked. Mario was atleast moving forward... I just measured my gc stick and it has a 30k ohm pot. I have tried with PS1 sticks that are 10k ohm and does didnt work at all, just like you described. Measure your gc stick, make shure its wired up right and hope for the best.
I did break my controller when I cut it and didnt rewire ground

, so dont forget that

What would be ideal I guess is to find a stick thats 50k ohm. Then its guaranteed to work

. I havent found one yet...
What Im using now in my new portable is an official nintendo controller and an Atmega8a that translates a potbased (modern) analog stick to the wierd crap nintendo controllers have. It works great with PS1 and gamecube sticks.
PS I made a thread just like this one when I had problems... No solution though

.
viewtopic.php?f=33&t=9759 Joey did post a link to a site that you can order from, but minimum order is 1000 pieces :/. Atleas that confirms that they do exist somewhere out there... DS