I am using Windows 10, and my Blizzard app shows in the taskbar (and I can right-click to open games), but the window itself will not show. I found some old posts where people have similar problems because of multiple monitors (real or virtual), but I only have one monitor and no virtual spaces that I know of. I only have one desktop in the task bar. The Blizzard App only has a blank square for the data (when alt-tabbing, mouse over the task bar, etc.).
Edit: I should add, I have also tried re-installing the app.