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 \approx 400 –600 hard X-ray ( \gtrsim 10 keV ) photons with NuSTAR , provided that these photons are not significantly absorbed ( N _ { H } \lesssim 10 ^ { 24 } 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 N _ { H } \approx 7 \times 10 ^ { 24 } 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 \alpha 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 \textrm { - - } 40 \% .