  We use the 4Ms CDF-S survey to place direct X-ray constraints on the ubiquity
of z~2 heavily obscured AGNs in K<22 BzK galaxies. Forty seven of the 222 BzK
galaxies in the central region of the CDF-S are detected at X-ray energies, 11
of which have hard X-ray spectral slopes (Gamma<1) indicating the presence of
heavily obscured AGN activity. The other 36 X-ray detected BzK galaxies appear
to be relatively unobscured AGNs and starburst galaxies; we use X-ray
variability analyses over a rest-frame baseline of ~3 years to further confirm
the presence of AGN activity in many of these systems. The majority (7 out of
11) of the heavily obscured AGNs have excess IR emission over that expected
from star formation (termed "IR-excess galaxies"). However, we find that X-ray
detected heavily obscured AGNs only comprise ~25% of the IR-excess galaxy
population, which is otherwise composed of relatively unobscured AGNs and
starburst galaxies. We find that the typical X-ray spectrum of the heavily
obscured AGNs is better characterized by a pure reflection model than an
absorbed power-law model, suggesting extreme Compton-thick absorption in some
systems. We verify this result by producing a composite rest-frame 2-20 keV
spectrum, which has a similar shape as a reflection-dominated X-ray spectrum
and reveals an emission feature at rest-frame energy ~6.4 keV, likely to be due
to Fe K. These heavily obscured AGNs are likely to be the distant analogs of
the reflection-dominated AGNs recently identified at z~0 with >10 keV
observatories. On the basis of these analyses we estimate the space density for
typical (intrinsic X-ray luminosities of L_X>1E43 erg/s) heavily obscured and
Compton-thick AGNs at z~2. Our space-density constraints are conservative lower
limits but they are already consistent with the range of predictions from X-ray
background models.
