It turns out that this was a firewall problem and not the
problem that I described in the post. Sorry about this.
Once a firewall rule was changed, it all worked fine.
To ddschwint... I received a "UPS Tech Alert" back in
November 2008. In the email was a line that said, "To find out if
your system supports SSL Version 3.0, please go to Online Tools
Support for detailed instructions."