"Troubleshooting Your Kindle DX" page at Amazon, under "Kindle screen frozen or Kindle unresponsive," it states:
Low battery charge.
- Plug the Kindle into a wall outlet.
- Ensure the Kindle is charging (the indicator light should be on).
- Wait 2 minutes.
- If necessary unplug the Kindle and reset by moving and holding the power switch for 20 seconds before releasing it.
You may not have held the power switch long enough to do a full reboot. It does take longer than 10 seconds on my Kindle Keyboard 3G (more like 30-60 seconds). I have read that you shouldn't do the restart procedure while the device is actually charging, so be sure to disconnect the Kindle before doing that.
I hope you'll be able to get it working again!