Instructions
Check to see if the AC adapter is fully inserted both into the back of the console and the wall outlet. The adapter connects to the Nintendo Wii through the DC input connector located on the bottom of the back of the console.
Disconnect the AC adapter from the wall outlet. Wait a couple of minutes and then plug it back in. Turn the Nintendo Wii power back on to see if it will work.
Check the batteries of the Wii remote if you are using the power button on the remote to attempt to power on the console. The batteries may have weakened to the point the controller will not operate properly.
Make sure the audio-video cables for the Wii are connected in the proper plugs on the back of the television. These usually come color coded in red, white and yellow to help with proper insertion.