Renormalization group (RG) procedures have been extended recently in phase-space cell approximation to predict, in addition to universal thermal properties observed asymptotically close to the gas-liquid critical point of fluids, also nonuniversal and nonasymptotic properties. This "globalized" RG theory is applied here, using a Lennard-Jones potential, to calculate the temperature, density, and pressure at the critical point of argon and to calculate pressures for a wide range of densities at temperatures close to, below, and considerably above that at the argon critical point. Choices required for the Lennard-Jones parameters and the quality of fit to experimental data suggest some of the strengths and limitations of the global RG theory.