I experienced this problem 3 weeks ago and my e-mail hasn't been the same since. I, like you, had to reset my password, then no mail at all because the server said I was on dial-up, then i couldn't & still can't send e-mail and now the server says the server uses a security certificate that can't be verified. Called 3 times for help and not much success, my yahoo works but I prefer outlook. I was told to use e-chat & was disconnected 3 times. Very frustrated & fed up
The on dial up thing.. is usually outlook itself.. sometimes if it cant conect, it changes HOW its trying to look for it.. trying a 'different' internet connection. three should be a setting to change this in outlook... i havent used it in a few years, so couldnt tell you exactly where.
For the certificate thing.. usually over time, many different types of sites which use secure connections have to update the certificate to keep secure. Usually everything is ok on PC end and updates auto, but not always.
One thing to make sure to do to help keep the PC end as up to date and can often help with the cert issues, is do all your windows updates. Some of those updates are root certificate updates which can help with those issues.