  We present near-infrared spectroscopy and narrow-band imaging at the
wavelength of redshifted H-alpha for a sample of 30 high-redshift, far-infrared
luminous galaxies. This sample is selected from surveys in the sub-millimeter,
millimeter and radio wavebands and has complete redshift coverage with a median
redshift of z~2.4. Removing obvious AGN, we find that the predicted H-alpha
star formation rates in this diverse population are suppressed (by ~10x)
compared to those derived from their far-infrared luminosities. We estimate
that AGN are present in at least 40% of the galaxies in our sample. To further
investigate this, we construct a composite rest-frame spectrum for both the
entire sample and for those galaxies which individually show no signs of
nuclear activity. We find [NII]/H-alpha ratios for both composite spectra which
suggest that the energy output of the galaxies is star-formation- rather than
AGN-dominated. The median H-alpha line width for our sample (removing obvious
AGN) is 400+/-70km/s (FWHM), and the typical spatial extent of the H-alpha
emission in our narrow-band observations is < 4-8kpc, which indicates a
dynamical mass of 1-2 x 10^11 Mo. This estimate is larger than recent estimates
of the dynamical masses of UV-selected galaxies at similar redshifts derived in
an identical manner. We also compared our H-alpha and far-infrared luminosities
with deep Chandra observations of a subset of our survey fields and use these
data to further assess their AGN content. We conclude that these high-redshift,
far-infrared luminous galaxies represent a population of massive, metal-rich,
merging systems with high instantaneous star formation rates, strong dust
obscuration and actively-fueled AGN which are likely to be the progenitors of
massive local elliptical galaxies. (abridged)
