To fix the issue, you need to disable certain antivirus features such as your firewall and check if that solves the problem. Sometimes your antivirus can interfere with Skype and that can cause problems while signing in.
Windows won’t end a task in Task Manager? If you’d like to fix the problem when Windows 10 won’t end task, there are ways to resolve it. Bear in mind that your chat logs will be deleted by using this solution, but you should be able to restore them from Skype.old folder if you need them.
Try starting Skype again and check if the issue is resolved.