We present infrared spectroscopy using a new array spectrometer on UKIRT of 11 radio galaxies at 2 < z < 4. We detected emission lines from all of them, principally the [O III] 495.9/500.7 doublet from the five galaxies at z > 2.9 and the Halpha, [N II] 654.8/658.3 complex from the galaxies at z < 2.9. For a number of galaxies we also obtained detections of one or more of the following lines: Hbeta, [O I] 630.0, [S II] 671.6/673.1. The ratios of luminosity in the [O III] doublet to radio luminosity are similar to the ratios for radio galaxies with lower radio luminosities, suggesting the line emission and the radio emission is being caused by active nuclei in both sets of objects. The Lyalpha/Halpha and Lyalpha/Hbeta ratios for these galaxies are congruent-to 10-20 times lower than the ratios predicted by photoionization models and are generally lower than the values of these ratios for low-redshift radio galaxies, implying greater extinction in the high-redshift sample. If the low values for the line ratios are caused by selective dust extinction to the line-emitting regions, the selective extinction of the continuum is likely to be at least as large and would be enough to explain the red optical-infrared colors of these objects. If the low line ratios are caused by the resonant scattering of the Lyalpha photons, the intrinsic Lyalpha equivalent widths of these objects are approximately 10 times greater than the maximum Lyalpha equivalent width that can be produced by stars, implying again that the gas around high-redshift radio galaxies is photoionized by active nuclei rather than by stars. The K-band magnitudes, which are crucial for determining the cosmological status of high-redshift radio galaxies, are seriously contaminated by emission lines, with contributions from the lines to the K-band fluxes ranging from 0%-100%. The contamination of the K-band magnitudes by strong emission lines means that the spectral energy distributions (SED) of radio galaxies at z > 2 are much bluer than previously realized, and in some cases are similar to the flat SED expected for a protogalaxy. Although it is impossible to use a blue SED to prove a high-redshift radio galaxy is a protogalaxy, it is possible to conclude (1) that for some high-redshift radio galaxies there is now no evidence for an evolved stellar population, and (2) that since these galaxies are necessarily young objects (for OMEGA0 = 1, at z = 3 it is only 1.7 Gyr since the big bang), the blue SEDs are strong circumstantial evidence that we are seeing some of these galaxies during their initial burst of star formation. There is a correlation between optical and radio luminosity at z > 2, which suggests there is a nonstellar contribution to the optical luminosities. The galaxies in which it seems there is most likely to be a nonstellar contribution have very red SEDs, implying that the probable effect of nonstellar emission is to make an SED redder. Therefore, besides line emission, there are two processes in a high-redshift radio galaxy which may be acting to redden the SED of the underlying starlight, and thus to conceal the cosmological status of the galaxy: selective extinction by dust and nonstellar emission. For OMEGA0 = 1 two radio galaxies with very blue SEDs have optical luminosities lower than expected from models for the passive evolution of a preexisting stellar population, and indeed optical luminosities that are similar to those of radio galaxies at zero redshift. If these galaxies are in a protogalactic phase, as is suggested by their blue SEDs, their low optical luminosities could be explained by them either being close to the beginning of the protogalactic phase or being also at an early stage of dynamical evolution. The optical luminosities of the other radio galaxies are consistent with their protogalactic phase having occurred in their past, but if, as seems likely, there are other processes besides simple stellar evolution occurring-dynamical evolution and nonstellar emission, for example-it is possible that some of these are also in a protogalactic phase.