  We use the S\'aez-Ballester (SB) theory on anisotropic Bianchi Class A
cosmological model, with barotropic fluid and cosmological constant, using the
Hamilton or Hamilton-Jacobi approach. Contrary to claims in the specialized
literature, it is shown that the S\'aez-Ballester theory cannot provide a
realistic solution to the dark matter problem of Cosmology for the dust epoch,
without a fine tunning because the contribution of the scalar field in this
theory is equivalent to a stiff fluid (as can be seen from the energy--momentum
tensor for the scalar field), that evolves in a different way as the dust
component. To have similar contributions of the scalar component and the dust
component implies that their past values were fine tunned. So, we
reinterpreting this null result as an indication that dark matter plays a
central role in the formation of structures and galaxy evolution, having
measureable effects in the cosmic microwave bound radiation, and than this
formalism yield to this epoch as primigenius results. We do the mention that
this formalism was used recently in the so called K-essence theory applied to
dark energy problem, in place to the dark matter problem. Also, we include a
quantization procedure of the theory which can be simplified by reinterpreting
the theory in the Einstein frame, where the scalar field can be interpreted as
part of the matter content of the theory, and exact solutions to the
Wheeler-DeWitt equation are found, employing the Bianchi Class A cosmological
models.
