Instead of showlog, you could try to run a little background script which monitors udev events. Here's some sample output (pressing the home button, followed by the power button).
Code:
[root@kindle root]# udevadm monitor --udev
monitor will print the received events for:
UDEV - the event which udev sends out after rule processing
UDEV [1326350407.129921] change /devices/platform/whitney-button/input/input3 (input)
UDEV [1326350412.356096] online /devices/virtual/misc/yoshibutton (misc)
Update: here's some more verbose log.
This could also allow you to check if your power button is really broken, or if there's possibly just some configuration oddity (probably unlikely though). In any case, if I were you, I'd return the device to Amazon for exchange if the power button is broken. Keep in mind that if it doesn't work, you have to be extremely careful not to brick your device, because it's often enough the only button you have left once it is broken. Just saying.