I’m assuming that you get the login screen with user name, password and the login button, but that if you click the button it just goes on showing you that screen. I wondered whether a broken page was lodged in your browser cache which is stopping the ‘logged in’ screen appearing even though you have successfully logged in. I’m not saying this is the explanation, just a guess. I’ve seen one or two glitches around password authentication so there may well be something else to look at.
Could you try to clear your browser cache to see if the issue is fixed?
Chrome: 3 dots top right – more tools – clear browsing data – make sure only Cached Images and Files is ticked
Firefox: History (top left) – Clear recent history – time range everything and make sure only Cache is ticked
Internet Explorer: Gear icon top right – safety – Delete Browsing History – make sure only Temporary Internet files is ticked