To troubleshoot the Wii controller, first ensure that the game you are playing is intended for that specific controller. Next, make sure that the controller is properly connected to the Wii game system's console. Resync the console, and attempt to use the device.
The easiest way to check if a game requires the classic controller is to visit the Wii shopping channel and browse for the game in question. If the controller applies, there should be a blue icon shaped like the controller next to the game's description.
Next, make sure that the device's connection to the console is as directed, and smooth out any kinks or knots from the cord. Restart the console, and allow it to reach the health and safety page; don't press the A button. Find the red Sync button on the left side of the console, hold it down for 15 seconds, and then resync all controllers according to original instructions.
Make sure all controllers have sufficient batteries; if not, replace. Select a game and game mode to test that require the classic controller. It is helpful to cross-test the console with a functioning Wii controller and the suspect controller with another console, if available. If the controller is still unresponsive, consult the official Nintendo site for accessory repair and replacement.