I'll need more details. you describe what should happen, so i have a good idea of the expected result, but you don't describe what actually does happen when try to log in, only that it doesn't work, I need more detail than that to be able to help determine what the problem is.
also, you don't include details on how the access rules are created.
What are the settings you mused for the Staff access rule? what about for the Governors rule?