There are competing theories. One of them, which is backed by some empirical evidence, is "Continuity of Mind" by Michael Spivey
http://www.amazon.com/Continuity-Mind-Oxford-Psychology/dp/0...
Short summary by Spivey:
http://www.cogsci.rpi.edu/CSJarchive/Proceedings/2003/pdfs/3...
Another approach, also relying heavily on experiments, is the "Grounded Cognition" thesis, of which Lawrence Barsalou gives a good summary:
http://www.psychology.emory.edu/cognition/barsalou/papers/Ba...
From the abstract:
"Grounded cognition rejects traditional views that cognition is computation on amodal symbols in a modular system, independent of the brain’s modal systems for perception, action, and introspection. Instead, grounded cognition proposes that modal simulations, bodily states, and situated action underlie cognition."
EDIT: I forgot a very interesting one involving a computational experiment:
Selmer Bringsjord, "A New Gödelian Argument for Hypercomputing Minds Based on the Busy Beaver Problem"
http://www.osl.iu.edu/~kyross/pub/new-godelian.pdf
Now I'm looking for evidence which supports your theory - that brains = minds = computers. Affirming that a theory exists without providing evidence that it is true is not enough.