Would a Human Mind in a Non-human Body Still be Human?

So, this is an interesting thought. If a human consciousness in its entirety were to be transmitted into some kind of non-human surrogate, would you regard that vessel as human? I guess another related question would be, "How much do our bodies play a role in making us who we are?" Of course, this also requires a definition of human. Personally, I think the affect of our bodies on our character and values is often underestimated. The body sets one's limitations and shapes how one experiences reality. I believe our mortality and weaknesses are fundamental parts of the human experience. So, I guess I would answer 'no' to this question. What do you think? Yes? No? It depends? For clarity, the surrogate could be either biological (like another species of animal) or non-biological (like a robot). However, I am gearing the question toward the non-biological scenario, but if you want to discuss the biological one, that's fine as well.