Susan Barnes includes Minsky's statement that "that biological human brain cells could be replaced with computer chips" in her examination of mind versus body. (pg 235) Minsky continues asking, "Would that new machine be the same as you?" Teri also posed a similar concern in her response.
I would argue it is. Assuming the computer chips are made without flaws, and enough knowledge had been gathered about the brain and designing the chips, there's no difference between a real person and a person (or cyborg) with one of these computerized brains. In essence, our brains already act like computers, though far more advanced than the current supercomputer. There's absolutely no reason given enough time, according to Moore's Law, we won't be able to program a computer with the capabilities of a neural network identical to the human brain.
To address Teri's concern, I don't think in the example we are arguing that a digital copy of one's self from yesterday will match today's self. Rather think of it like this (and assume sufficient technologies exist): Suppose one day, an evil genius snatches you up, and through the wonders of (post)modern technology, exactly copies your self to a little computer chip and replaces your brain. However, he also erases any memory of his devious little experiment. When you woke up the next morning, would you, or for that matter anyone, be able to tell your self had been digitized? (Ignore the giant scar.) I would argue no.
In Barnes's writing, I get a sense of fear of this future. She seems hesitant to believe that a digitalized version of one's self is equal to the original, biological source. She argues for the necessity of a "real" body to develop one's sense of self.
However, a "real" body is no longer necessary. In a biological setting, the body only exists to provide stimulus for the "mind." Now, in a digital age, such physical bodies are no longer necessary. There's no physical body necessary, if it can be replaced by digital bodies created in cyberspace. A brain in a vat will have just as much self as any other "real" person, maybe even more given any stimulus is possible.
Now, combine these ideas together. I would argue at some point in the future, we will have digital lifeforms, either purely in cyberspace or in robotic form, indistinguishable from "real organic life." They will think, act, and live in the exact manner as ourselves. They will meet or exceed our own intelligence. There's absolutely nothing stopping this future, nor should there. At some point the human species will die off, but through our digital creations, our legacy may continue.