Rhino Mocks ignore private method

Rhino.Mocks (as well as most of the other free mocking frameworks like moq) can't mock non-virtual members. As @Joe Tuskan said, you should either wrap the functionality in an interface and inject the interface in the constructor or make it a non-static method that can be mocked.

If you've got money to spend, there are commercial mocking tools that allow non-virtual members to be mocked. I don't have any experience with any of them so I won't mention any by name.