Thanks, Inland.
I read the article, unchecked the Update Root Certificates box in Add/Remove Programs / Add/Remove Windows Components, and OKed out.
Restarted the system normally - it seemed to take a little less time to shut down.
When that was finished, rebooted into Safe Mode and opened a Command Prompt window. Since I didn't have anything I wanted to do, I just typed Exit and pressed Enter to close the Command Prompt window.
Tried to reboot and, once again, the system froze at the Windows is shutting down screen.
After I got the system back up, I checked the Event log. There have been no more Error entries since the 2 early yesterday morning, so it seems that problem has been resolved.
BTW, I did an Internet search on "can't reboot from Safe Mode in Windows XP". All of the results were about either how to reboot into Safe Mode or not being able to boot into Safe Mode or Normal Mode - not a single one about not being able to reboot
from Safe Mode.
Thanks much for your help so far. If you (or anyone else) have any further suggestions, I will appreciate them.

Jema