Hello my name is***** will be assisting you today. I am sorry to hear that you are having such trouble. I will try my best to help you.
Sir/Ma'am are you trying to open the inbuilt Skype in windows 10 or the desktop version of Skype?
Other than it showing you to sign in page does it show any error message?
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Other than it showing you repeatedly the sign in page does it show any error message like incorrect login id or password?
Are you using a Skype id or Microsoft live id to login to Skype?
Do you still have access to the email account that you used for opening this Skype account?
Sir/Ma'am checking to see whether you still need my help with the Skype issue if so please let me know by answering the above questions so that I can help you better.