I know you've uninstalled and reinstalled the games several times. Have you tried the 'repair' option found when right clicking the title? Or the 'update' option after redownloading? You may need to download a patch to get the DLC to work. I'm not super technical, but these are just some ideas. I hope one of them works for you.
Worth a shot. Sorry it didn't work. I'm not very technical.
There is this post: http://answers.ea.com/t5/Dragon-Age-Inquisition/DAI-GOTY-gift-Origin-DLC-Problem/td-p/5722721 which seems to have been working for others.
@rellkan posted, "Just an update for anyone that is experiencing this issue and happens to stumble across this thread; EA support seems to be aware of the issue, because after explaining the problem, my CS agent deleted the gifted copy of the game and replaced it with a new version that now works as it should. Cheers." in that thread. I hope this helps.
So if your CS agent seems to be reluctant to do that, you can refer them to that post if they are unaware of that fix.
