To some extent the scientists and the non-scientists are arguing somewhat at cross purposes. You seem to be arguing, as I am, that a system can be said to be deterministic if we can model it - that is, if we can set up a computation that predicts its behavior. By this standard, sure, Brownian motion is not deterministic; and if it will ever feasible to model a human brain, we're a long way from even being able to demonstrate the possibility.
Alamo-Girl is taking a Platonist view; that if the system works according to a set of physical laws, it is deterministic, because it's theoretically possible (even if utterly infeasible) to predict its behavior at any point in time. As I noted earlier, QM says that if the wavefunction of the universe is psi, then d psi/dt is just -i*hbar*H*psi, and it's just a very big Runge Kutta problem. :-)
Maybe we should make a distinction between empirical determinism and essentialist determinism.