Had something similar myself a year or so ago. Couldn’t find a way round it, and Hotmail were worse than useless in their help. All they could say to me was “give the answer to your security question”. Unfortunately they wouldn’t tell me what the question was – I was supposed to remember it from when I opened the account. They finished up telling me to report to “your local law enforcement officials” before they would help. I gave up and went elsewhere.
Sorry if it’s not what you want to hear, but it was a right pain.