new sticks are replaced but register in one direction and don't move

From the description it sounds like there could be a short in one or the solder joints on one of the potentiometers or "pots" (the green plastic part of the stick assembly that has three prongs). Take a look at each of the solder joints using a microscope or a cell phone camera and see if you can spot any issues where two or more of the posts are accidentally soldered together. If one or more are found, simply remove the excess solder and that should clear it up.

If no solder problems are found, check each pot's mounting onto the stick assembly. They are attached with plastic clips so they can be separated from the assembly with a spudger or small driver bit or something. Just press on each green pot to ensure that each is clipped properly to the sides of the stick assembly.

Finally, it is also possible that the replacement pots were nonfunctional before they were installed. If the other options end up being ruled out, then this the likely case. If it is, just desolder the pot or pots in question and solder new ones on. There should be no need to replace the entire assembly unless the stick itself sticks or is otherwise broken.