Can you open I.E.
Start Button -> All Apps -> Windows Accessories -> Internet Explorer
and go to Outlook.com and access your account and outlook email from there?
IF so then that would indicate that there is not a problem with your account and perhaps the problem is with your local profile instead.
Can you create a new user account as a member of the local administrator's group (not a standard user) and log in with that new account and see if your problems persist, especially opening Edge