Make sure you have configured the "GameCube Controllers" section in Dolphin. From the main screen, click on the Graphics icon (or use from the menu choose Options -> Controller Settings). Set Port 1 to Standard Controller. Click on the Configure button to assign input from your gamepad.
A lot of times, people mistakenly configure Wii Remote controls, but not GameCube controls (which are separate in Dolphin). I know you've said you've configured the controls, but this is a common enough occurrence that it always helps to double-check.
If that doesn't help, could you please show us screenshots of your controller configuration? Preferably the screen you get when you click on the Graphics icon, and the actual button assignments.
A lot of times, people mistakenly configure Wii Remote controls, but not GameCube controls (which are separate in Dolphin). I know you've said you've configured the controls, but this is a common enough occurrence that it always helps to double-check.
If that doesn't help, could you please show us screenshots of your controller configuration? Preferably the screen you get when you click on the Graphics icon, and the actual button assignments.