I proceeded in the following order:
- Uninstall Norton Security (subscription had expired, no longer needed)
- I already had the Windows 10 installation files on a thumb drive, so I went ahead and did the upgrade to Windows 10 (hoping that would magically fix the connectivity issue)
Something in Windows Firewall was preventing network connectivity. Just to be certain, I enabled Windows Firewall ... and it broke again. I did not want to leave Windows Firewall off permanently (not a good idea, particular for a laptop that will be used on public networks). From Control Panel's Windows Firewall section, I clicked the "Restore Defaults" link to restore Windows Firewall to its original, default settings. After that, WiFi worked just fine (with Windows Firewall enabled). I cannot say for certain what Windows Firewall settings were causing the problem - but I can confirm that disabling Windows Firewall, and subsequently restoring the default settings, resolved the issue.
I am grateful for the divine inspiration that helped me get this issue resolved.