  [Abridged] We investigated the X-ray characteristics of the Class I YSO Elias
29 with joint XMM-Newton and NuSTAR observations of 300 ks and 450 ks,
respectively. These are the first observations of a very young (<1 Myr) stellar
object in a band encompassing simultaneously both soft and hard X-rays. In
addition to the hot Fe complex at 6.7 keV, we observed fluorescent emission
from Fe at $\sim6.4$ keV, confirming the previous findings. The line at 6.4 keV
is detected during quiescent and flaring states and its flux is variable. The
equivalent width is found varying in the $\approx 0.15--0.5$ keV range. These
values make unrealistic a simple model with a centrally illuminated disk and
suggest a role of the cavity containing Elias 29 and possibly reverberation
processes that could occur in it. We observed two flares, with duration of 20
ks and 50 ks, respectively. We systematically observed an increase of $N_H$
during the flares of a factor five. This behavior has been observed during
flares previously detected in Elias 29 with XMM-Newton and ASCA. The phenomenon
hints that the flaring regions could be buried under the accretion streams and
at high stellar latitudes, as the X-rays from flares pass through gas denser
than the gas along the line of sight of the quiescent corona. In a different
scenario, a contribution from scattered soft photons to the primary coronal
emission could mimic a shallower $N_H$ in the quiescent spectrum. In the
spectrum of the full NuSTAR exposure, we detect hard X-ray emission in the band
$\approx20-80$ keV in excess with respect to the thermal emission. The hard
X-ray emission could be due to a population of energetic electrons accelerated
by the magnetic field along the accretion streams. These particles could concur
to pumping up the Fe fluorescence of cold Fe of the disk along with X-ray
photons with $E>7.11$ keV.
