Hmm... A "definite maybe" doesn't sound very convincing
Anyway, as I see it the brain is fully capable of making decisions even without any input from the "outside", as a decision really isn't anything else than millions of synapses colliding (both consciously and uncounsciously). But it really only leads us to the original problem. The only way for you to have a fully independent free will is if it does not consist of atoms (like a soul, or any similar supernatural matter). As I see it, at least, the brain consisting of atoms is what limits everything and makes every decision explainable (no matter how extremely complex it would be to actually explain them).
However, I must admit that I'm not an expert in English, so I might have just missed your point entirely xD. If so bear with me.
It's a definite maybe because I don't know enough of brain research and cognitive psychology to give a definite answer either way :)
But, my point is that if you want to go to the (sub)atomic level, you need to change your definition of free will. And because of the Heisenberg uncertainty principle, and the quantum effects, you can never go to the (sub)atomic level and then construct the system back from there.
In other words, precisely because free will is not (or can't be proven to be) different from matter, it needs to be looked at as a system, not as a singularity. So the question is: does the system, as a whole, have free will as per your definition? And remember, a system is, by definition, a collection of dependent elements so it does not matter how the system functions in the inside.
I don't know if I can explain what I mean well enough. I'm just working with your definition of free will, and that definition combined with what we know of the brain and our consciousness leads me to the conclusion that our consciousness can be autonomous and independent. That the internal processes are both deterministic and random does not matter based on that definition.