If you are attempting to login with the correct account name and password and are being told that there is not an account with that name, the account has been closed.
If no one else has opened an account with that username, you may be able to create a new account with that same name, but it might not be possible to open a Hotmail account now that outlook.com has replaced Hotmail.
Your best option is probably to go to
http://windows.microsoft.com/en-US/windows-live/id-support
and click on "My problem isn't listed here."
Re: Facebook... Try the Report a Login Issue form at
https://www.facebook.com/help/contact/357439354283890
More Facebook Help:
Search or post a question at
https://www.facebook.com/help/community
Don