May 2020
Hey! I checked everything and I still have the same error with Firefight Pack. Actually, after I deleted the DLC folder I could not repair the game twice - had an error (327682:0). Then tried to relaunch Origin with administrator rights and the repair was done successfully.
I launched the game, had the same error, but now I also have problems with the Galaxy At War map/info - it just doesn't load/connect:
However, I can play the multiplayer just fine (tried it and played one game). So I have no idea what is the problem there...
Also when I relaunched Origin (without the administrator rights) and the game, Origin again started to repair the game and finished it without problems this time.
Oh, and I tried the new game - it works, though I didn't even go to character creation screen, just checked if the game would allow me to start it.
So, still no progress (and now Galaxy At War is broken as well :D)...
May 2020
The "Galaxy at war" problem is global, not just on your end. JFYI.