A self-consistent, nonperturbative theory, developed to describe the structure and thermodynamics of a classical system of particles and presented in a previous paper [Phys. Rev. E 65, 016131 (2002)], is generalized to a two-dimensional system and applied to the square-well potential. The theory predicts a phase diagram which turns out to be in very good agreement with that obtained by computer simulations performed by us. This is a consequence of the very accurate results of the theory as concerns the angle-averaged two-body distribution function and the Helmholtz free energy, which we also present and compare with computer simulations. By contrast, a first-order perturbation theory only provides qualitative agreement, showing that higher-order terms play an important role and that these terms are well accounted for by the nonperturbative theory.