I left it overnight and charging all morning. Then I found this thread -- www.amazon.com/forum/kindle%20customer%20service%2...
It appears others are having this problem as well.
The good news is the solution suggested above worked for me. That is:
- Hold down the power button for ~30 seconds
- Release and press the power button again
The charging light will light up and then it will do a reboot (all data is preserved).
Anyone have any idea why it freezes up like this? This was the first time it happened for me...