That could be a problem with the remote syncing. If your wii turned off/went into standby on its own, the wii remote could have lost signal and could not sync with it when you tried that morning to turn it back on.
I think you should either turn your wii all the way off by holding down the button until you have a red light. I think leaving it on all night might have caused something to overheat? Thats just my guess.