What browser and version are you using? I've just checked, and I can sign in (all on Windows 7) with:
Firefox 60 (64-bit)
Chrome Version 67 (64-bit)
Internet Explorer 11 (32-bit)
I'd try clearing your browser cache and if that doesn't work, try a different browser.
When you say that "it shows that I am signed in" do you mean that it shows your email address and the words "Sign Out" in the upper right corner next to the Microsoft logo (see screenshot in my earlier post)? What do you click on at that point that takes
you back to the sign-in page?
Or are you referring to this pop-up window, and if so, which option do you select:
