How can I recover my MS Office 2011 product key?
This is an old thread, but I ran into this issue and the way to fix it is as follows:

You have to be able to access the hard drive you migrated from.
Make sure all Office programs are closed.


On the new hard drive/computer you migrated to, delete the following file:

/Library/Preferences/com.microsoft.office.licensing.plist  

Go to the HD you had a working copy on, and copy that same file from the same location to the new HD.

It should have an older date from when you installed it and activated it.