The observational data of the Orion Nebula Cluster (ONC) is reanalyzed by means of new sets of pre-main sequence (PMS) evolutionary tracks including rotation, non-gray boundary conditions (BC's) and either low (LCE) or high convection efficiency (HCE), aiming better understanding of the appropriate physical constraints for the rotational evolution of the stars within the ONC. The role played by convection is a key aspect of our analysis, since there are conflicting results from theory and observations. We derived stellar masses and ages for the ONC by using both LCE and HCE and considered was the role of non-gray atmospheres. Our results show that the resulting mass distribution for the bulk of the ONC population is in the range 0.2-0.4M⊙ for our non-gray models, and in the range 0.1-0.3M⊙ for gray models. In agreement with previous works, we found that a large percentage (∼70%) of low-mass stars (M≤Mtr, where Mtr is a transition mass) in the ONC appears to be fast rotators (P<4days). Mtr depends on the model choosen, being Mtr=0.5 for LCE, Mtr=0.35 for HCE and, as found in previous works, Mtr=0.25 for gray models. Finally, our analysis indicates that a second parameter is needed for a proper description of convection in the PMS phase.