The successful fabrication of a nanocomposite in bulk form consisting of a randomly oriented assembly of nanoscale sized core-shell particles has required an increased understanding of the theoretical aspects of the thermoelectric transport properties. Our particular nanocomposite consists of a nanorod core in 1D quantum confinement coated with an outer conducting polymer shell. Upon fabrication of the bulk composite, these nanorods are embedded within a three-dimensional conducting polymer matrix. We address the nanorod thermoelectric components by assuming a single parabolic band within the one-dimension density of states. Both elastic and inelastic scattering of electrons or holes is accommodated by solving the variational form of the Boltzmann transport equation. An altered lattice thermal conductivity for the confined nanorods is calculated separately to account for boundary scattering that is important in low dimension structures. Exact expressions for the bulk effective electrical and thermal conductivities, Seebeck coefficient and figure of merit are then obtained through the field decoupling transformation, which is a special case of two-component composites. Our method is easily generalized to any two component composite of spherical or cylindrical microstructure and is independent of the materials bulk geometry. The results similarly apply to one, two or three dimensional transport regimes with or without quantum confinement merely by solving the appropriate fundamental transport equations for each constituent material. Comparison to experimental data is then presented which helps validate the nanocomposite theory.