As was discussed in the previous (related) blog post "Troubleshooting Exchange 2010 Management Tools startup issues", in Exchange 2010 the Management tools are dependent on IIS. As was discussed in...
Updated Apr 22, 2020
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Blog Post
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Resolving WinRM errors and Exchange 2010 Management tools startup failures
Case solved !
I added new IP addresses to the network adapter for new websites on the IIS 7 - it seems this has started the problems. I just found a hint on that in this article:
http://social.technet.microsoft.com/Forums/en-US/exchange2010/thread/5f6950b0-7215-479d-9e5e-fb93c76699ce#5f6950b0-7215-479d-9e5e-fb93c76699ce
http://social.technet.microsoft.com/Forums/en-US/exchange2010/thread/5f6950b0-7215-479d-9e5e-fb93c76699ce#5f6950b0-7215-479d-9e5e-fb93c76699ce
After changing the bindung for the Default website in IIS from a specific address (the one which was present at installation of Exchange) to "All unassigned" the Exchange Mangement GUI reacts normal now !
Hope this is useful for others with such problem.