On the right side of my screen there is an approximate “1 inch X 4 inch” rectangular dead area. My cursor changes to the shape it has when I am on my Windows home screen. I cannot issue any commands in this area. It persists in all game modes in HoTS. This issue is unique to HoTS and does not exist in any other games that I play. I have uninstalled the game several times. I have tried to use the 'Scan and Repair" function as well.
Hello DRINKBEERNOW 
This sounds like some program with overlay functionality, or a pop-up notification, is interfering with that patch of screen space. The best way to approach this would be to shut down non-Microsoft programs that boot up automatically:
Closing Background Applications
When you identify which program was causing the issue, you can decide if it should be uninstalled, or check its settings/options for overlay or notification toggles.
Best of luck in your adventures 