I do use multiple monitors on my desktop PC indeed, so I'm going to try what you suggested.
Edit: no luck
Seriously considering reinstalling Windows 10 at this point. I suspect it's probably another program I have installed, but I have so many that it would take donkies to go through each.
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So I went ahead and did a full Windows reset, and now I have managed to get WoW running, waiting for the remainder to download and then I can download Overwatch and hope that runs!