I just discovered this same issue -- I had not played DAI since September 2015, and fired it up again today (5/2/16). I'm running Windows 7 like OP. Origins installed a patch (I assume the one from October 2015, which according to the patch notes should not have affected screenshots) before I began playing.
Now when I click the printscreen button, nothing happens. Not a black image, just nothing showing up at all. I do not believe the images are being taken, because previously there was always a small hitch in the frame rate when a screenshot was taken. Other than that, I never had any issues taking screenshots before today.
To troubleshoot I have:
* rebooted the machine
* verified that I am running in borderless windowed mode
* switched to regular windowed mode and back (no difference)
* verified that the resolution of the game matched the resolution of my monitor
* verified that the printscreen button on my machine works (by using alt+tab to paste the results into Paint)
* searched for the files (in case they ended up elsewhere) on the entire machine ("ScreenshotWin32_*_Final")
No luck. Any suggestions?