The Classic Controller is used primarily for playing specific Virtual Console games downloaded from the Wii Shop Channel. Make sure the game you are attempting to play uses the Classic Controller by looking for the following icon on the game's description page on the Wii Shop Channel.
Verify that the Classic Controller is properly connected to the Wii Remote. Click here for more information.
If the Classic Controller is still not responding as it should, please contact Nintendo Consumer Service for more information.