i have the same issue. and the live chat agent asked me 4 questions and i had to answer 2 sets and my answers were not matching so they did not reset it for me.
My Skype was just hacked and my email was changed without my permission, how do I recover my account?!
In your case, you need to contact customer support. They may ask you to answer some verification questions to prove that you indeed own that account, before they can assist you in resetting your password - Just open the link pasted below to see the instructions on how to get in touch with customer service -