I have the same problem with my Kindle 3 (alias Kindle keyboard) and I had tried to hold the power switch button for 20 to 30 seconds but it did not work! Bummer!
It sounded like I have to power-cycle the device. I guess I have to open it up, test the power-switch, then power-cycle the device if the switch is good.
There is a guide that shows how you can open up this kindle on this site.