what dawkins is saying - and it is perfectly rational, perfectly descartian - is that our thoughts and feelings and behaviours must be wholly determined by everything else that's ever happened in the universe, before hand. it's a literal statement of determinism.
but, if we acknowledge that we are all unique entities, that our brains are autonomous identities in the sense that we are standalone organisms, then the question of free will reduces to the question of whether the experiment is repeatable - and some doubt needs to be cast on the question.
in perfectly controlled conditions, will humans always react the same way? it's really not an empirical question. and, while a descartes or a locke would have said "clearly.", our understanding of determinism is a little different, post-heisenberg.
our brains are computers, but they are not turing machines. they must be quantum computers, because they follow the rules of quantum mechanics, but we don't even understand the functioning well enough to state as much in any meaningful sense.
if we can come up with some kind of demonstration that our brains do not respond identically to identical stimulus, and that whatever randomness that occurs is localized to us as standalone organisms, then free will may find itself brought back from the brink by the uncertainty of quantum physics.