Can you received text messages on your phone? usually they'll send you a 'code' that you enter to get back into your account and reset your password.
Hotmail gets hacked easy, so when you get back in, create a strong password, and change your backup questions and answers. And double check the phone # they have on file.
The issue with your computer - is it browser related? Which browser are you using?
Internet Exploder? Chrome? Firefox?
Usually clearing out the cache/cookies helps with stuck issues like this. Ccleaner
is a great tool for this if you want to download it and try it.
Try running the registry portion as well, it might help.
If none of that helps, send me a PM. I do remote PC assistance for my side-work, I can give you a hand...