How are you attempting to reference the hotmail? Are you using Windows Live Mail? Are you using a browser to access it directly? Which browser? 32-bit or 64-bit version of the browser?
WLM has issues for many users so please try logging in to hotmail directly. Hotmail requires java scripting to work so if you have any script blockers it may also be causing the issues.
What I would suggest is going to accessories and running the
Internet Explorer (No add-ons) option and type in
www.hotmail.com or
www.live.com and attempt to login to your account.