This is really a subjective question, what one person thinks is human another might say is not and perhaps in the future will be coded into law.
The Turing test comes to mind which means a computer that passes the test could be considered human, right?
However if someone were to see the computer then only if it looks human, has human-like skin and hair and acts like a human then we would view it as human.
Back to your question, my guess is if the person retained his brain and memories then he/she would still be considered human although recently I read an article where the heart plays a major role in providing input to the brain so it may be needed too. Now you could dice the brain down to smaller components as long as the memories were retained then the person would still be a person which then brings you to a computer that can retain your memories.
So in the end, maybe its our memories that make us human no matter what hardware or wetware technology is used.