I also have a problem with Skype that I can't fathom out.
I have Skyped my brother in Australia twice a week almost since the days of dial up internet connection speeds. I last spoke to him last Monday with no problems. Today, I tried to open Skype of my Fujitsu AH530 Laptop and I couldn't sign in. All I was faced with was the rotating circle of dots that carried on until I stopped it. I deleted Skype and downloaded it again. I already had the latest version installed. I still could not sign in.
I engaged in an online "chat" with a Skype help adviser. He asked for remote access to my PC. I watched him going through various files and deleting various things. Eventually all went quiet. Losing patience I open the chat page and it had been disconnected quoting that as I hadn't used it for two minutes it had been closed. Whatever he may or may not have done I still couldn't sign into Skype.
My wife has an almost identical laptop to mine, a later model AH512, that she never uses since she got an iPod. I use it occasionally to keep the battery charged and updates installed. I switched it on and signed into Skype immediately using my same sign in details that wouldn't work on my laptop.
I had my chat with my brother using Google Hangouts which worked perfectly.
Has anyone got any clue as to what's gone wrong?
I'm using Windows 10.