To some extent yes, our choices and scope of action is constrained by our essential nature, some of which is determined before we are even born. However this doesn't absolve us of all accountability. It simply sets up a framework within which we can discuss what accountability is and how we want to manage it.
This is a difficult issue and I don't have all the answers about accountability, I see my take on it as my starting point for the discussion about it not the end. I believe in rehabilitative rather than retributive justice because of this. Also see my reply to fjuerfilis.
I think that morality, love and justice emerge from human nature. I think that I, my self and my consciousness are emergent properties and I'm fine with that. I think that the purpose of human life is chosen for us by the rules of biology, natural selection, game theory and a host of other factors that, seemingly miraculously, lead me to the conclusion that the philosophical Good Life is desirable and largely attainable.
In No Country for Old Men a guy flips a coin to decide if he will kill someone. He chose to flip the coin though - delegating a choice to randomness does not abrogate us of responsibility. By doing so he created the framework in which the outcome arrises, whatever that outcome is. He made it possible, even likely and bears responsibility for that by selecting the set of possible outcomes and the degree of randomness. Also he does this many times, so it wasn't a "random choice to randomly choose", it's a consistent repeated pattern of behaviour that directly emerges from his personal ongoing mental state.
I don't go around randomly killing people and that's a consistent pattern that emerges from my persistent ongoing (if evolving) mental state and it _is_ a free choice. The fact that it's pre-determined is fine, because it means it comes from me.