The following error message was fixed in an update to Office for Mac 2011:
"Sorry, there is a problem while trying to connect to your account. (Error code:0x8a010101)"
Here's how to get the latest updates:
How to get the update if you can start Office for Mac 2011
Open an Office program like Word, choose Help > Check for Updates and choose the Check for Updates button.
How to get the update if Office for Mac 2011 won't start
Download and install the Microsoft Office for Mac 2011 14.6.4 Update. You can then check for additional updates from within Office as described above.