My sense of awareness is a result of the chemical reactions occuring in my brain and body. Cease those reactions and I'm done, whether or not identical reactions are going on elsewhere. Similarly, if I can transfer all the physical parameters of my brain to a computer, including memories, thought patterns and the like, that's still not me on the computer. Let's go one step further. As far as I'm concerned I'm now sitting on a lab bench while some intruder brain has taken over my body.
Awareness is all about brain function.
Think of it as Brain v 2.0. Only version 2.0 will operate orders of magnitude faster and allow expansion modules. We appear to be approaching an age when the very nature of human individuality will be challenged and the possibilities are at once exhilerating and terrifying. Or for a darker view, let Sun's Chief Scientist, Bill Joy, explain Why the Future Doesn't Need Us . If the middle of the road is more to your liking, take a look at Societal Implications of Nanoscience and Nanotechnology, the final report of a workshop sponsored by the National Science Foundation.