Your Exchange Online (O365) tenant was recently upgraded to the new release of Wave 15. After which Users are not able to access their mail via OWA.
Once you sign-in to the MOP -> Click Outlook. It goes Blank, does not show anything and Inbox is not accessed.
This issue will occur if you are using IE8 on the machine. Mostly you will face with XP machines who are still on IE8 and not upgraded to IE9. As of now this is a known issue with IE8 performance and Wave15 O365
Upgrade to IE9 or above for better use of latest Wave15 features and Functionalities.
Note:- If you are not facing this issue and there are other issues with your O365 tenant after upgrading to Wave15, please contact Microsoft Support.