Just checked on my rogers connection.. Entered login info.. took about 3 seconds of a blank screen, but then did load the email screen. This is using win7, IE11
Now, the only difference i MAY have, is that i am using the google DNS servers? Though, that you can get to the LOGIN page.. wouldnt think the DNS would be a problem.. unless there are some major re-directs to different specific mail server names, etc which the DNS would be failing on.
I had this same problem with my MSN.COM e-mail for the past few days. Hotmail.com was not affected by whatever this problem was.
My problem was limited to web access for Microsoft e-mail/calendar/people and ONedrive. Whenever I tried to log on I just got the spinning wheel and nothing happened after that. I was able to access my e-mail thru Outlook 2007 thick client and also thru Windows 8/8.1 MAIL/CALENDAR/PEOPLE METRO app.
I too tried to use Google DNS vs Rogers to see if it helped but it did not make a difference so it was not a DNS issue.
I opened a support ticket on the microsoft web site 3 days ago and it took a while to get a response and the Microsoft tech asked me to do a trace of my login issues with a utility i had to download the sent the the results. Sometime today the problem went away and am back to normal.