  We report the discovery of two sources at z=3.867 and z=3.427 that exhibit
powerful starburst and AGN activities. They benefit from data from radio to X
rays from the CFHTLS-D1/SWIRE/XMDS surveys. Follow-up optical and near-infrared
spectroscopy, and millimeter IRAM/MAMBO observations are also available. We
performed an analysis of their spectral energy distributions to understand the
origin of their emission and constrain their luminosities. A comparison with
other composite systems at similar redshifts from the literature is also
presented. The AGN and starburst bolometric luminosities are ~10^13 Lsun. The
AGN emission dominates at X ray, optical, mid-infrared wavelengths, and
probably in the radio. The starburst emission dominates in the far-infrared.
The estimated star formation rates range from 500 to 3000Msun/yr. The AGN
near-infrared and X ray emissions are heavily obscured in both sources with an
estimated dust extinction Av>4, and Compton-thick gas column densities. The two
sources are the most obscured and most luminous AGNs detected at millimeter
wavelengths currently known. The sources presented in this work are heavily
obscured QSOs, but their properties are not fully explained by the standard AGN
unification model. In one source, the ultraviolet and optical spectra suggest
the presence of outflowing gas and shocks, and both sources show emission from
hot dust, most likely in the vicinity of the nucleus. Evidence of moderate
AGN-driven radio activity is found in both sources. The two sources lie on the
local M_BH-M_bulge relation. To remain on this relation, their star formation
rate has to decrease. Our results support evolutionary models that invoke radio
feedback as star formation quenching mechanism, and suggest that such a
mechanism might play a major role also in powerful AGNs.
