The 2-D electron system (2DES) in Si metal-oxide field-effect transistors (MOSFETS) consists of two distinct electron fluids interacting with each other. We calculate the total energy as a function of the density n, and the spin polarization ζ in the strongly-correlated low-density regime, using a classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge terms. Here the ten distribution functions, arising from spin and valley indices, are self-consistently calculated to obtain the total free energy, the chemical potential, the compressibility and the spin susceptibility. The T = 0 results are compared with the 2-valley Quantum Monte Carlo (QMC) data of Conti et al.(at T = 0, ζ = 0) and found to be in excellent agreement. However, unlike in the one-valley 2DES, it is shown that the unpolarized phase is always the stable phase in the 2-valley system, right up to Wigner Crystallization at rs = 42. This leads to the insensitivity of g * to the spin polarization and to the density. The compressibility and the spin-susceptibility enhancement calculated from the free energy confirm the validity of a simple approach to the two-valley response based on coupledmode formation. This enables the use of the usual (single-valley) exchange-correlation functionals in quantum calculations of MOSFET properties provided mode-coupling effects are taken into account. The enhancement of the spin susceptibilty calculated from the coupled-valley response and directly from the 2-valley energies is discussed. The three methods, QMC, CHNC, and Coupled-mode theory agree closely. Our results contain no ad hoc fit parameters. They agree with experiments and do not invoke impurity effects or metal-insulator transition phenomenology.