Ok so now you have to look over your firewall settings if you have the Windows Firewall or other program running to see if that is not allowing WLM as an exception. One way to verify the present protections are not the cause would be temporarily shutting them down long enough to make a few more attempts at logging in if you haven't already tried that out.
The page you can come across at the WindowsLivehelp site is very familiar to the Dec. 2009 posting seen at Error: 8100030d - Windows Live
Apparently they finally got around to updating the support information on the help site. But that was also the same page you posted at the start of the thread.
The question now would be the particular firewall and av protection you are presently running if not AVG as referred to on those pages? The FAQs section at the software company's own support site may also have a few things to try out.