In Windows (NT/2000/XP), you can "lock" the desktop which requires a user 
to enter a password before they can use it. In such situations, it's 
common that the PC will accept VNC connections, but they won't work: you 
supply a password, and the session immediately closes.

To work around this, setup VNC to run as a "Service" on the PC. It's one
of the options you'll see in the "Start -> Programs -> VNC" program group.

Sometimes even if you have it running as a service, the connection will
immediately close or you'll get a "connection refused" message. To fix
this, you may have to either stop and restart the VNC service, or uninstall 
and then reinstall VNC. Typically one of these two approaches will fix 
the problem.                                                               

Thanks to John Aldrich (JAldrich-at-covista-dot-com) and Sean Echevarria
(Sean-dot-contact-at-creepingfog-dot-com) for the info!