I had same problem (OIG would not work, no matter what. No access to DLC or MP). I originally had Origin in Beta mode. Rolled it back to normal, no dice. Tried windowed mode, no luck. Ran Origin & DS3 as Admin, and no luck. Already had vsync on, but tried turning off. I tried turning on OIG support for all games. Other games seemed to work (BF3, Crysis 2 & 3). I basically tried everything everyone mentioned in these forums, except on this topic I noticed the "open port" solution I hadn't tried. I figured it couldn't hurt. I looked at my settings, and my IP was 2.4, and port 3568 was open from Origin.
I noticed this forum poster, peterhero7, posted a youtube link, and said 3569 should be open. I didn't follow the youtube directions exactly, as I just opened port 3569 (UDP) for the IP my PC had right now which was 2.10 (not 2.4 like Origin had opened). I added this, and it worked. Still haven't went back to Beta version of Origin, but I reverted/played with all other settings, and works fine now. Also, I shut my PC down everytime I'm done using it, as it's only on 3-4 times a week. I imagine I will have to repeat this fix when I actually decide to play co-op, but now I know I can. I was actually trying to check for pre-order bonuses a friend from the UK said he got with this game, but I don't see them on mine, unfortunately.
I know you may know this isn't your issue, but I thought the same. Give it 2 mins & try it. You may be surprised. Thanks for starting this thread, as web searches were coming up empty for such an immediate issue (which I assumed was related to Humble Bundle people swarming the game).