Hi. PC user here.
I'm also having trouble logging into the EA servers. I think this started about a week ago for me. I originally had extreme trouble getting logged into the FIFA13 EA servers. Sometimes getting through. At the same time I could never log into the Cerberus network on ME2 (I play through Steam). This didn't bother me too much as I was just at the end of my second playthrough of ME2. As I've now finished ME2 again, I wanted to buy the DLC's for ME3 and start my second playthrough there as well, but it's the same problem as with ME2. Can't log into the EA servers. As this game is on Origin, I really can't fathom what's wrong on my end. These games were working fine not long ago. No issues with EA servers (except hic-ups with FIFA13, but that's been consistently bad). I haven't done anything drastic with my computer either that I can remember... Just normal stuff like AVG updates, graphic card drivers, windows updates etc.
So, no solution from me, but I wanted to let you know that you're not alone.
PS: The games run fine though (except FIFA13), so no big worries, except for getting DLC's for ME3.
PPS: Come to think of it, my Steam account is acting up as well... Always being in offline mode. Hmm.