Literally just fixed this by following this comment:
"Below I'm reposting what I wrote on the EA forums. I should warn you in advance that although this had some success with desktop users experiencing the fullscreen problem, many laptop users reported that the software features needed to correct the problem were not present in systems using NVIDIA's mobile GPUs.
I believe I have a solution. I can't guarantee it will work for everyone, but it has fixed this problem (for me at least) consistently in the past. The root of the trouble seems to be in the interaction of the Frostbite Engine with the NVIDIA display driver. I've run into this on Battlefield 3, BF4, and now Dragon Age: Inquisition; previously on my GeForce GTX 670 and more recently on my GTX 970.
Here's what I've done to fix it: first exit DA:I completely. Then open the NVIDIA Control Panel. On the right of the main window, under the Display tree, click Adjust desktop size and position. In the center of the window you should now see two tabs, make sure the one titled Scaling is selected. Inside this view, under Select a scaling mode, you should see several radio buttons representing the various scaling options. If No scaling is currently selected, try selecting Full-screen scaling instead. If Full-screen scaling is already selected (but full-screen is nonetheless non-functional in DA:I), try toggling one of the different options on instead. In the bottom right corner of the Control Panel, click the button labelled Apply. Then relaunch DA:I and set the game to run in full-screen mode. If the first time doesn't fix the game, quit the game, and try one of the other two scaling options in the control panel - try each option before you give up. Hopefully one will fix your problem.
Cheers, and good luck!
*Edit: Since I can't include an image directly in my post, here's a link to a screenshot that highlights the relevant section in the NVIDIA Control Panel."
taken from here: https://forums.geforce.com/default/topic/800459/geforce-mobile-gpus/dragon-age-inquisition-cant-go-full-screen-/2/
woo hoo!
