You bring up some very important questions, and ones that are not easily addressed in a Christian context. These are complex issues which, unfortunately, some have tried to provide overly simplistic answers. I can tell from your question that you have already thought very deeply about this yourself, so it is likely that my response will only move the bar slightly for you. Your comments about monism vs dualism are appropriate. At one time, I was quite close to the Descartes dualist camp. I thought the answer to what a human being is was quite simple. I am a soul/spirit which occupies this body temporarily. However, this view is not complete and it does not comport with biblical theology. I learn from 1 Corinthians 15 that our bodies are part of what and who we are. We are not “brains on sticks.” But we are certainly not just a body. We are persons. We have free will. We have a spiritual nature. We are souls with bodies. Everything I know about human beings is consistent with the idea that we were made in God’s image, and this part of us is not a physical thing, as God does not have a physical body.
But I have not even started to address your question. Yes, behavior is, in part (but not on the whole) biological. If we get cancer or suffer a traumatic injury to certain parts of the brain, it absolutely does affect our personality, and our personality is part of who we are. But…. The fact that we are biological beings and that who we are is determined, in part, by biology does not “prove” that we have no soul or that we do not have an eternal nature or that we are not spiritual beings any more than the fact that we are spiritual beings proves that we are, in our essence, not biological beings. Dualism simply does not work. By the way, I am also not a strict monist. My body will die, but I will occupy a different sort of body (1 Corinthians 15).
The fact is that not only can our personality radically change due to TBI and chronic illness such as cancer, it also is changed by aging. You did not mention Alzheimers, but you could have! Like the dual questions of evil and suffering (which are at least as much different from this question as they are similar, but there is some similarity), the issue raises serious questions for which there is no simple answer and, in the end, faith in God has to be part of the answer. Does a person who has had a deep faith and repentance and been baptized into Christ and saved lose her or his salvation because that person later becomes senile and begins to act in an extremely unchristian way? Logic struggles with this question, but faith speaks to this. I have faith in the justice but also in the love and mercy of God. I say that God can handle this just fine. I am confident that my friend of several years ago who went through this exact process due to illness did NOT lose her salvation. I also believe that people who suffer from life-long serious mental disabilities remain innocent, as they were, in essence children and not accountable.
The scientific materialist and the determinist use this question that you raise to “prove” that we are merely bodies–a sack of chemicals, neurotransmitters and a neural network, but they are wrong. We are persons. Justice is not simply a meaningless word. It is immoral to rape and to murder. There is hope. Jesus was raised from the dead. We are truly and wonderfully made in God’s image, and the fact that we are biological does not disprove any of these contentions, no matter what these committed materialists say.
I know that I have not fully answered your question, but I hope this is at least helpful.