Thanks GrampaJohn. I will try this on my new Cambio that is 1 month old and having the same non-working power button problem too. I will post if it fixes the problem after I know more. I also wanted to note that I did NOT select the fast start-up as an option...it must be a factory default setting, but it was "checked" when I went to my power settings, so I un-checked it and hope this fixes it.
One other item I noted when I was checking out the power settings is: there are default settings for what pressing the power button accomplishes (there is a separate setting for power button response in battery-mode versus plugged-in mode). For some reason, the default setting for both these were "hibernate", which supports your theory that the computer is hibernating instead of powering down. The only issue, in my case, is I don't turn off my computer using the power button, I use the windows menu to shut-down my computer, but the result appears to be the same, meaning the computer appears to turn off (even though it might only be hibernating, as it turns out), then the power button doesn't work next time I try to power on. So I changed those default settings to "turn off the computer" when the power button is pressed (whether I am on battery or plugged in) instead of having the power button "hibernate" the computer.
Anyone else having this problem might try these fixes too.