Huh thats weird I had that problem at first with the 360 controller back when I was trying to get it working. All 1001. The first thing I decided to do was update the drivers, then after a restart it worked... Now for that gamecube controller idk what to say. If your analogs work with the gamecube controller then by all means use Joy2Key with that instead. The next thing i would say if your absolutely sure all your drivers are up to date and stuff, try a clean download of Dolphin, make a separate folder and configure it all again. It might not hurt to try and run it in compatibility mode for windows xp sp2/sp3. Try that let me know what you get.
OH! Shoot try this! Settings -> Gamecube tab -> Port 1 should be set as "Standard Controller" see if that clears things up. I had you setting that to dummy controller, but that works for me not u.
OH! Shoot try this! Settings -> Gamecube tab -> Port 1 should be set as "Standard Controller" see if that clears things up. I had you setting that to dummy controller, but that works for me not u.