  We present the results of recent Chandra, XMM-Newton, and Hubble Space
Telescope observations of the radio-loud (RL), broad absorption line (BAL)
quasar PG 1004+130. We compare our new observations to archival X-ray and UV
data, creating the most comprehensive, high signal-to-noise, multi-epoch,
spectral monitoring campaign of a RL BAL quasar to date. We probe for
variability of the X-ray absorption, the UV BAL, and the X-ray jet, on
month-year timescales. The X-ray absorber has a low column density of
$N_{H}=8\times10^{20}-4\times10^{21}$ cm$^{-2}$ when it is assumed to be fully
covering the X-ray emitting region, and its properties do not vary
significantly between the 4 observations. This suggests the observed absorption
is not related to the typical "shielding gas" commonly invoked in BAL quasar
models, but is likely due to material further from the central black hole. In
contrast, the CIV BAL shows strong variability. The equivalent width (EW) in
2014 is EW=11.24$\pm$0.56 \AA, showing a fractional increase of $\Delta EW /
\langle EW \rangle$=1.16$\pm$0.11 from the 2003 observation, 3183 days earlier
in the rest-frame. This places PG 1004+130 among the most highly variable BAL
quasars. By combining Chandra observations we create an exposure 2.5 times
deeper than studied previously, with which to investigate the nature of the
X-ray jet and extended diffuse X-ray emission. An X-ray knot, likely with a
synchrotron origin, is detected in the radio jet ~8 arcsec (30 kpc) from the
central X-ray source with a spatial extent of ~4 arcsec (15 kpc). No similar
X-ray counterpart to the counterjet is detected. Asymmetric, non-thermal
diffuse X-ray emission, likely due to inverse Compton scattering of Cosmic
Microwave Background photons, is also detected.
