Thank you all for the most insightful and helpful replies. This has been most useful.
What started this question was that we once had a total flight control pitch and roll jam while attempting to perform the pre-take off flight control check. This got me thinking about what alternate means of controlling the airplane might be available.
In trolling around the internet, I found and nice but more detailed overview than in our manuals of the flight control architecture. I can't post the URL here because I am a new poster, but if you Google search "B777 ACES" it comes up.