Cannot access Hotmail using Firefox or IE, different error messages

HP desktop, Windows7, most recent Firefox and most recent IE as browers, Orange Telekom 3G net connection (slow but adequate).

Accessing Hotmail with Firefox, the access terminates with TLS message about Unsecured Connection due to the website having out of date authentication certificate. Using IE, I get the login page, enter account name and password and get a message saying connection failed because I am not connected to a network. Huh? Logging into MSN.com with the same account name and password, I can see links to recent mail in Outlook but when I click the link, am again told I have no network connection.

Any suggestions?