Three-dimensional time-dependent quantum calculations have been used to study the nonthermal desorption of CO physisorbed on a rigid NaCl(100) surface. The three strongly coupled degrees of freedom are CO physisorption, libration, and translation along the surface. The wave packet is expanded in a discrete variable representation basis and is propagated in time using the Chebyshev expansion algorithm. Nonthermal amounts of energy have been put into both the CO librational and translational modes at t=0, while the physisorption mode was placed in the ground state. The probability of desorption and the corresponding unimolecular rate coefficients have been computed for a variety of initial states with different translational and librational quantum numbers. The results are compared with our previous work, where molecular translation was not considered. We find that the inclusion of the latter degree of freedom significantly lowers the librational desorption threshold, though some librational energy still needs to be present at t=0 for desorption to take place. The inclusion of molecular translation also causes the appearance of desorption from previously "dark" odd librational states and significantly accelerates desorption from "bright" even librational states. We have also observed the translational "saturation" effect at fixed values of the librational quantum number; namely, the desorption probability becomes insensitive to further increase in translational excitation starting with the translational quantum number=3. Librational motion has been shown to play a mediating role in energy transfer between the translational and physisorption modes.