I'm experiencing the exact problem described above. When I boot the game, it shows me as logged out. Upon entering my email address the Origin toolbar takes me to the sign up page rather than recognizing my login. After sitting on that page for about 30 seconds the game delivers a "Can't connect to Origin" pop-up and then returns me to the sign up page.
The funny thing? If I enter my actual Origin username in the sign up box, it errors out and tells me my username has to be a certain character length. It's amusing that this is occurring during a big cross media promotion with tomorrow night's Treehouse of Horrors episode. Poor EA. The only thing that company is good at is dropping the ball.
Can't say I'm that upset. After hearing about all the technical problems the game experienced at launch (especially with lost progress) I never bothered to spend any money on it. After experiencing them myself, I never will.