Many of the problems I've been having are explained in great detail on this forum post. Like many others, I've tried uninstalling and reinstalling the game, turning off firewalls and anti-viruses, and several other tricks that normally fixes this sort of thing. I'll quote what one person has said on that forum post right here:
I'm at the point where a specialist is trying to help me with the issue.
The person had me do a trace to see if the connection is blocked anywhere--which I assume meant to see if it was blocked on my end. The trace showed all packets getting through just fine, except one point that had an IP address listed to EA was dropping %100 of packets. So, the specialist told me the issue has gotten stranger and that the trace was clear. And now the person wanted me to send in a file of my system information.
Yet, still the issue is being considered to be on my end. I suppose it'd be nice if it ended up being something I can fix. But each time it's showing nothing being wrong on my end.
I'm also to the point of getting someone to look at my PC and find out if I have problems with my firewall or something like that, I'm currently downloading the game onto my laptop just to see if I can log into the origin servers from there. In my case, the problems may all be on my end and perhaps it does sound like I'm pointing the finger at the "bad guys" when its not your guys' fault that my computer just needs a little repair or a security program is being over-zealous. However, I seriously doubt that is the case for many of the other people having the same difficulties I'm having, as well as other problems.
That being said, hearing a community manager finally say something is definitely appreciated and I hope some of these issues get resolved soon. I may have come across as a bit of a flamer in this post, but only because I am such an avid fan of Bioware's products. The matter has been frustrating for me and what appears to be several other people in the community, but I truly wish you and whoever is working to resolve these issues the best of luck on doing so.