I know this will probably get a copy/pasted answer regarding cleaning buttons or needing to send it in for repair. So if that's you're answer, please don't paste it. Those are clearly not the problem. Now with that out of the way, let me explain what's going on.
The gamepad will not turn on the console. This is similar to what is described in this thread: http://techforums.nintendo.com/thread/19889. The gamepad can, however, turn off the console, so this is clearly not an issue with dirty buttons as one uses the same button to turn on and off the console. It seems like a software issue. What's interesting is that other non gamepad controllers can turn the console on. Any idea on how this software issue can be fixed? is there a setting somewhere I need to change? I tried powercycling the console and that did not work.