Misunderstanding may arise by confusing the Buddhist and scientific definitions of death. Within the scientific system you spoke quite validly of the death of the brain and the death of heart. Different parts of the body can die separately. However, in the Buddhist system, the word death is not used in that way. You'd never speak of the death of a particular part of the body, but rather of the death of an entire person. When people say that a certain person died, we don't ask, "Well, which part died?"
If you are tossed about by doubts, full of strong thoughtless passions, and yearning only for that which is detrimental, your thirst will grow stronger and stronger, unquenched, and your pain will grow with your defilements.
There is, Oh Monks, a not-born, a not-become, a not-made, a not-compounded. Monks, if that unborn, not-become, not-made, not-compounded were not, there would be no escape from this here that is born, become, made and compounded.
We need a sense of the oneness of the 7 billion human beings alive today. When I meet people, I don't think about being different from them, about being Tibetan, Buddhist or even the Dalai Lama. I only think about being a human being. We all share the potential for positive and negative emotions, yet one of our special qualities is our human mind, our intelligence. If we use it well we'll be successful and happy.
Basically, the Buddhist attitude is that you should not accept certain things through sheer faith. And for that you need a skeptical attitude. Buddha himself made this clear to his followers. He said you should not accept those things I taught out of respect for me, but rather through investigation by yourself.
And he who has considered all the contrasts on this earth, and is no more disturbed by anything whatever in the world, the Peaceful One, freed from rage, from sorrow, and from longing, he has passed beyond birth and decay.
The Tempter masters the lazy and irresolute man who dwells on the attractive side of things, ungoverned in his senses, and unrestrained in his food, like the wind overcomes a rotten tree. But the Tempter cannot master a man who dwells on the distasteful side of things, self-controlled in his senses, moderate in eating, resolute and full of faith, like the wind cannot move a mountain crag.
The many factors which divide us are actually much more superficial than those we share. Despite all of the things that differentiate us - race, language, religion, gender, wealth and so on - we are all equal concerning our fundamental humanity.