Got locked out of my Outlook email account

Last night I got an email saying somebody had tried to log in to my Hotmail/Outlook email address. Today, when I try to get in, I’m asked to Verify my account. So I go through the process of Verifying my account:
1-Have them send a code to my alternate email address, which is already in their records.
2-Go and get the code, then go back to the Microsoft Verify page and enter the code they sent me.
3-Create a new password.
4-Log in again.

And I get the locked out/Verify message all over again. I’ve done this six times now.

I found Microsoft customer support’s automated help system, which just sends me to the Verify page again. I tried to contact a live person, by phone or by chat, but in every attempt, they want me to log in to my Microsoft account. That’s my problem, I can’t log in to my account.

I found a page where people talk about Microsoft problems, and have found a couple of other people with the same verification runaround, but no solutions.

Any ideas?