We're all having trouble getting into Origin and Answers HQ right now. The Anthem demo opened a few hours ago, and people are having trouble accessing it, so they're swamping other EA platforms.
In the meantime, can you take your computer completely offline and then try logging into Origin? Your account info should be stored on your computer, unless you've recently cleared Origin's cache. When you attempt to login while you don't have an internet connection, Origin is supposed to automatically put itself into offline mode and then use its stored data to validate your account credentials.
