You're off topic for this forum, which is dedicated to Windows Live OneCare, but the most common reason for not being able to login with your LiveID would be a local issue.
Try deleting temporary Internet files and cookies from your Internet Explorer (or other web browser) tools/options and then try logging in again.
If you are unable to access your email account, but can log in elsewhere, then contact Hotmail support:
http://support.live.com - select Windows Live Hotmail from the available programs.
-steve