Towards the end of September, Microsoft a published one Update for the latest versions of Windows operating systems, including Windows 8.1.
Some users complained that after installing the updateKB4038792, the connection between their computers and the Microsoft account (outlook, MSN, live, exchange) was interrupted.

KB4038792it's an update “cumulative” what does it bring for Windows 8.1 besides fixing / solving security problems and other improvements. Therefore, it will be quite difficult for users to detect which part of this update prevents the authentication to the Microsoft account. Apparently, it is some kind of firewall, which effectively blocks the connection between the laptop / PC and the Microsoft Account.
“Sign in to your Microsoft account
Sorry we couldn’t connect to Microsoft services right now. If this problem persist, search for “network problems” on the Start screen“
This authentication problem was confirmed on September 22, 2017, by a Microsoft official, after a user reported on September 16, 2017 on the support forum, that he could no longer authenticate on his Microsoft account after the KB4038792 update. The problem was reported on an HP 2G 250 laptop with Windows 8.1.
Microsoft recognizes this problem, which according to the company, affects a relatively small number of users in certain areas and with systems / PCs that have some common elements. Not identified yet.
As a solution for users who use the account Microosft for authentication on Windows 8.1, is to use the local account until this bug is resolved.
Microsoft promised that it will try to fix this problem as soon as possible.
Thank you very much for this post, I had installed Windows 8 to see if I could get a free license (update) to Windows 10, and I didn't know what to do to solve the problem and what was happening, you explained it to me. the idea is that I have an older version of Windows 8.1, so I don't understand why it wouldn't work for me because I didn't do that update, but please
It is most likely also a problem with Microsoft's authentication servers, which is why your authentication is not working.
However, if you access in the browser, are you able to authenticate?