The human brain absolutely IS a deterministic computer. (on some level)
Choice is based on available data. That data may be from any combination of possible sensory and memetic inputs, but no decision is made in a vacuum. We may not -- yet -- know the specific algorithms that determine, for example, the choice of a mate. We know many of the factors that can contribute: specific hormone levels, societal norms, etc, and any Advertising exec can program the vast majority to buy unrelated stuff based on those inputs.
To use poor old Pavlov as example, the mind can be trainied in very specific ways. If brains were non-deterministic, there would be equal chance that ringing a bell would cause salivation and homicidal rage.
The brain is a black box. There is nothing to say we can't build our own black box that does the same thing.