How to get to a real person (they're called "Game Advisors") to help at EA Customer Service.
[EDIT: Feb 1, 2014] They've changed the process, and changed the urls!
Go to the EA Help Center and fill-out the required information, (Product/Problem/Platform).
Then look for the "Chat Now", "Call Me", or "Email Now" buttons. (Not the AHQ "Ask Now" one, unless you want to ask fellow gamers in the self-help forums. )
(The specific options you see may vary depending on your region and the time-of-day.)
If you select "Chat Now", be sure you have enough time (at least one hour) to wait before being connected to someone.