My problems are over. I am documenting how for the next person who runs into the same vexing situation.
After having spent considerable time with Microsoft's "Troubleshooting Windows Home Server Connector" and running Microsoft's "ConnectorTroubleshooter.exe" (part of the Windows Home Server Toolkit), I came to the conclusion that the problem was most likely connected to permissions. I tried the resolutions suggested in Microsoft KB article 939218 which is referenced in the Troubleshooting paper. (The brief description of certificate errors in the Troubleshooting paper raised more questions than it answered). The 939218 solutions did not work and generated Access Denied errors.
So what worked? Microsoft's Subinacl permissions fixer.
For full instructions on this utility for repairing file and registry permissions, check out Aaron Stebner's blog at
http://blogs.msdn.com/astebner/archive/ ... 39820.aspx
for complete instructions and useful commentary.
The reset.cmd Aaron provides is very powerful medicine. You should back up your registry before running it. It can be useful in dealing with installation problems and pesky Internet script errors caused by incorrect access control permissions.