Configuring preferences and options in Outlook.com
To whoever still has this issue, the best way to fix it is not to "reconnect" but to DISCONNECT your account, and then actuallyre-connect it yourself. I reconnected using the link I got with the e-mails several times, I decided to disconnect entirely, then connect it again. To my surprise, it worked.
The only question that remains is, why couldn't Microsoft make a reconnect algorithm that is capable of doing this for you...
I did that before, and now I can't use outlook.com messages to talk with gtalk friends. I'll try do this again, but I know the result.