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I haven’t used the Terminal Services Web Client for a few years and when I installed it on a Windows 2000 server with the latest updates applied I received an “Object doesn’t support this property or method: ‘MsTsc.Server'” error.
After a bit of research I found that the problem dates back to some security updates from 2002 (for further details, see the Remote Networking Development website and/or Microsoft knowledge base article 328002 and/or Microsoft security bulletins MS02-046 and MS02-047). Downloading the latest Remote Desktop Web Connection fixed the problem and my servers are now available from wherever I happen to be.
Thanks! You solved my problem!