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)
http://www.filedropper.com/profileoptionsprofile
