Same here, in my case, yesterday my computer was shut down due to a power outage at my neighborhood, so I went to sleep. Today when I start happens this problem only with Galaxy (Steam works well and the other applications I had opened).
May be due that wrong shut down? Or it is a general problem? I'm on Windows 10.
This is the message:
"Oops! Something went wrong. Click below to log in to GOG Galaxy".
There is nothing to click, the rest of the window is black.
A lot of people are having the same problem.