Yesterday, I realized that it could be just that the Palm had locked up in a way that it was burning battery power, and it had therefore drained the battery.
I called Lori up and asked her to change the batteries, and when she did, the Palm came back to life. Whee!
All its state, of course, was on our desktop computer, which has been having its own problems.
After Kevin came over and confirmed that he couldn't cure the desktop computer's woes, I kept restarting the computer for a while in hopes that it would work long enough to restore my Palm from backup.
After much frustration, I managed to successfully log in to the desktop and start a restore.
After several minutes of restoring, I grew complacent and tried to open a browser window. This was a mistake--the desktop locked up with the Palm only partially restored. I didn't manage to successfully boot up the desktop again.
The Palm hasn't been in good shape today. It's been going unresponsive from time to time, and spazzing out in other ways when I try to get its attention. Sigh...