But does it actually connect? In the bottom left corner at the main menu, do you only have the shortcut to Dragon Age Keep or is there also a "Log In"?
At the main menu in Options -> Account, do you have the "Always log me in" selected? If so, you could try unselecting it and then clicking "Log In" at the main menu (in the bottom left corner). If that doesn't work - there might be something wrong with your internet connection.
Though that gives me a thought - do you play with Origin in offline mode? If so, changing that may help, I've never played in offline so I can't be sure if it prevents from connecting to the servers.