After upgrading a Windows 8-based desktop PC to Windows 10, I started seeing the regular error message: "Failed to connect to a Windows service: Windows couldn't connect to the Group Policy Client service. This problem prevents standard users from signing in."
This issue, as the message states, prevented users other than the Administrator from logging in or, if they managed to login, prevented them from doing very much. This was an intermittent issue that seemed to be occurring on an increasingly frequent basis.
I found the fix for this on the Windows 10 Forums thread Can't connect to Group Policy Client service where windowsmith advised turning off "Fast Startup." As documented in The Pros and Cons of Windows 10's "Fast Startup" Mode, "Fast Startup ... doesn’t always work perfectly, and there are some downsides that might convince you to turn it off." Turning off "Fast Startup" has led to a much more positive experience using our Windows 10-based desktop.
Several sites explain how to disable/enable Fast Startup including the post that helped me realize this was the issue I was facing. The gist of the approach is to use Start → Settings → System → Power & sleep → Additional power settings → Choose what the power button does → Shutdown settings → [uncheck] Turn on Fast Startup (recommended). I have "Fast Startup" checked/enabled on my Windows 10-based laptop (came from Windows 7) without any obvious negative issue, but "Fast Startup" seemed to cause far more trouble than any achieved benefit on my Windows 10-based desktop.
Since unchecking/disabling "Fast Startup", I haven't seen the "Windows couldn't connect to the Group Policy Client service" for over a week and I formerly saw it almost daily.