I'm not sure what the cause of that error on signin would be, but I can tell you that you need to use the *same* LiveID on this activation as you used on the original or it will ask you for payment.
Since the error reports that it is having problems making the connection to the servers to login, it may be worth reviewing this:
See this post for the KB article to troubleshoot install problems - http://social.microsoft.com/forums/en-US/onecareinstallandactivate/thread/ba26b781-da18-4ce4-be8c-22647bd5d8fc/
The problem could be as simple as a setting in IE for "automatically detect" being enabled on the Connections tab.
If you are still unable to sign in for activation, please contact support:
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare Forum Moderator