  We present NuSTAR hard X-ray observations of two X-ray weak broad absorption
line (BAL) quasars, PG 1004+130 (radio loud) and PG 1700+518 (radio quiet).
Many BAL quasars appear X-ray weak, probably due to absorption by the shielding
gas between the nucleus and the accretion-disk wind. The two targets are among
the optically brightest BAL quasars, yet they are known to be significantly
X-ray weak at rest-frame 2-10 keV (16-120 times fainter than typical quasars).
We would expect to obtain ~400-600 hard X-ray (>10 keV) photons with NuSTAR,
provided that these photons are not significantly absorbed (NH<1E24 cm^{-2}).
However, both BAL quasars are only detected in the softer NuSTAR bands (e.g.,
4-20 keV) but not in its harder bands (e.g., 20-30 keV), suggesting that either
the shielding gas is highly Compton-thick or the two targets are intrinsically
X-ray weak. We constrain the column densities for both to be NH~7E24 cm^{-2} if
the weak hard X-ray emission is caused by obscuration from the shielding gas.
We discuss a few possibilities for how PG 1004+130 could have Compton-thick
shielding gas without strong Fe K? line emission; dilution from jet-linked
X-ray emission is one likely explanation. We also discuss the intrinsic X-ray
weakness scenario based on a coronal-quenching model relevant to the shielding
gas and disk wind of BAL quasars. Motivated by our NuSTAR results, we perform a
Chandra stacking analysis with the Large Bright Quasar Survey BAL quasar sample
and place statistical constraints upon the fraction of intrinsically X-ray weak
BAL quasars; this fraction is likely 17-40%.
