If you haven't already tried disabling origin in game, downloading the latest video driver, repairing the game, reinstalling directx from the DA:I redist folder, etc. might help.
If you have tried the above, see if the game will launch doing this,
Navigate to your 'Documents>BioWare>DragonAgeInquisiton>Save' folder
Rename your 'ProfileOptions_profile' file to 'ProfileOptions_profile bak'
Then download this version of the file into the folder, (It has the video options set to low, resolution 1280x720, and windowed mode)
I had this same problem, disabling Origin in the game fixed it.
My games > DA:I > Click on the letters "Dragon Age^TM: Inquisition > Game Properties > Check "Disable Origin for this game"
From DeathToSquid on this thread:
