I had a problem with my Office for Mac activation not being recognized. It had worked on this machine for a few months with no problems, and I don't know what I did or what update could have caused it to stop working but it did. I looked at many forums and help areas, but no suggestions worked. Today I first used the Microsoft Chat who then referred me to their Office for Mac help line, 800-642-7676 they were very helpful. Here is the solution given that worked for me, I hope that it will help others.
go to "login.live.com"
sign in to your account
under "Account" select "Security and password"
look for "Two-step verification"
If it is turned "On" then turn it off.
Now go back to your Office application and your sign-in should work just fine.
The Microsoft Rep said that I could turn the 2 step verification back on once I had signed in again, but I think I will leave it off for now.