Same here. New Mac Book Air. Office 365 University. UK. Can access (but not Access ;o) Microsoft account without issue. I looked at the certificate issue referenced above, but there are no blue crosses. I'm going to phone MS, despite this being a well reported
issue, in an effort to get them to pull their fingers out and sort the issue.
So far I've had to order a new Windows 8.1 pro (to dual boot) and then buy Office 365, just to open a single Access file. Not great.
Update: After speaking with Microsoft Mac Tech Support:
"I understand. I'm sorry to hear that. As of the moment, this is an emerging issue as of the moment. And the Office for Mac department already advised us to try to activate your Office every after 2 hours
This is still being investigated by our Office for Mac specialist with regards to this issue."
Thankfully, it works perfectly on Windows 8 Dual boot with VMWare.
Good Luck Everyone!
Update 2: I'm not getting the specific error message now. Instead, when I try to sign in to activate I get:
"Sign in failed because the password is incorrect or the sign-in name does not exist."