A recent Chandra/ACIS observation of the Orion Nebula Cluster detected 1075 sources (Feigelson et al. 2002), providing a uniquely large and well-defined sample to study the dependence of magnetic activity on bulk properties for stars descending the Hayashi tracks. The following results are obtained: (1) X-ray luminosities L_t in the 0.5-8 keV band are strongly correlated with bolometric luminosity with <log L_t/L_bol> = -3.8 for stars with masses 0.7<M<2 Mo, an order of magnitude below the main sequence saturation level; (2) the X-ray emission drops rapidly below this level in some or all stars with 2<M<3 Mo; (3) the presence or absence of infrared circumstellar disks has no apparent relation to X-ray levels; and (4) X-ray luminosities exhibit a slight rise as rotational periods increase from 0.4 to 20 days. This last finding stands in dramatic contrast to the strong anticorrelation between X-rays and period seen in main sequence stars. The absence of a strong X-ray/rotation relationship in PMS stars, and particularly the high X-ray values seen in some very slowly rotating stars, is a clear indication that the mechanisms of magnetic field generation differ from those operating in main sequence stars. The most promising possibility is a turbulent dynamo distributed throughout the deep convection zone, but other models such as alpha-Omega dynamo with `supersaturation or relic core fields are not immediately excluded. The drop in magnetic activity in intermediate-mass stars may reflect the presence of a significant radiative core. The evidence does not support X-ray production in large-scale star-disk magnetic fields.