Please follow the below mentioned steps which could fix the issue:
Go to www.hotmail.com --> Click on "Can't access your account?" --> Select "I forgot my password" --> Click on "Reset your password" --> Enter your Hotmail ID --> Enter the given Captcha --> Select "Customer support" --> Then below that you will be getting an option "Customer support", click on it -->
Enter your working E-mail ID and follow the instructions.
Note: No Need of filling "Billing Information"
If issue still persists, try changing the browser. I would suggest you install the Google chrome and then try opening the Hotmail account on Google chrome.
Please reply with the results and any further questions.
Thanks & Regards