Due to the Bekenstein bound and other constraints, our brains aren't even Turing complete. At best, we're finite state automotons (with a large set of states). Also, your characterization of free will is incorrect:
The basic question is whether we are able to make decisions for ourselves or whether the outcomes are predetermined and the notion of choice is merely an illusion.
The free will debate in philosophy is about defining free will. You can't just assume the above definition of free will = non-determinism, because then you've already set the premises framing the debate, and so we already know with reasonable certainty that we don't have this sort of free will.
Compatibilism is a definition of free will which is compatible with determinism, and with this paper. For a more accessible reference, it's also the notion of free will you'll find in the Matrix sequels, ie. programs and people like Neo can see into the future, but don't necessarily understand what they see until they've gathered enough context to understand why their future selves make the decisions they do.