You don't happen to have a long password for your Windows Live ID, do you (longer than 16 characters)?
I ask, because I've seen that choke the process of signing in before. If you do, try changing the password to something a little shorter (16 characters or less) and see if that works.
If you already had a short password, does your internet connection go through a proxy (say at a workplace)? I've also seen this be a problem.