This is likely either related to the latest Windows 10 update or a third party conflict. I recommend trying steps 1-3 below and retest:
Step 1) Goto your Documents folder -> Delete the Diablo III folder at this location to clear the game's settings.
Step 2) Goto the Blizzard app -> Select the Diablo III tab -> Options -> Drop down to: Show in Explorer -> Open the Diablo III folder -> Right click on Diablo III.exe -> Properties -> Compatibility tab -> Check: Disable Fullscreen Optimizations. Apply and Ok. Do the same for Diablo III Launcher.exe.
Step 3) Right click on your desktop -> Select: Display Settings -> Change your Resolution to a notch down, apply and save the change. Run the game, it should run. If it does change your Operating System resolution back to normal, run the game again to update the game's resolution.
If the issue remains try playing in Selective Startup mode to shut down all background programs and avoid any conflicts. Make sure your display drivers for the system are fully updated if you need help with this step check out our support page Here.