did you spill anything on it?
Maybe the sensor bar is the problem, since the buttons work?
I don't know what to tell you other than that. I don't know why it would shut down when you hook up a peripheral to the controller, unless it's just a defective wiimote...
Edit: Check this sticky thread:http://www.wiichat.com/nintendo-wii-...-problems.html
Maybe something there will help you?
Also, here's another sticky with Nintendo Customer Service links: http://www.wiichat.com/nintendo-wii-...r-service.html