  We present JVLA observations of the cold (CO (1-0)) molecular gas in IRAS
F10214+4724, a lensed ULIRG at z=2.3 with an obscured active nucleus. The
galaxy is spatially and spectrally well-resolved in the CO (1-0) emission line.
A CO (1-0) counter-image is detected at the 3-sigma level. Five of the 42 km/s
channels (with >5-sigma detections) are mapped back into the source plane and
their total magnification posterior PDFs sampled. This reveals a roughly linear
arrangement, tentatively a rotating disk. We derive a molecular gas mass of
M_gas = 1.2 +- 0.2 x 10^10 M_sun, assuming a ULIRG L_{CO}-to-M_{gas} conversion
ratio of \alpha = 0.8 M_sun / (K km/s pc^2) that agrees well with the derived
range of \alpha = 0.3 - 1.3 for separate dynamical mass estimates at assumed
inclinations of i = 90 - 30 degrees. Based on the AGN and CO (1-0) peak
emission positions and the lens model, we predict a distortion of the CO
Spectral Line Energy Distribution (SLED) where higher order J lines that may be
partially excited by AGN heating will be preferentially lensed owing to their
smaller solid angles and closer proximity to the AGN and therefore the cusp of
the caustic. Comparison with other lensing inversion results shows that the
narrow line region and AGN radio core in IRAS F10214+4724 are preferentially
lensed by a factor >~ 3 and 11 respectively, relative to the molecular gas
emission. This distorts the global continuum emission Spectral Energy
Distribution (SED) and suggests caution in unsophisticated uses of IRAS
F10214+4724 as an archetype high-redshift ULIRG. We explore two Large Velocity
Gradient (LVG) models, incorporating spatial CO (1-0) and (3-2) information and
present tentative evidence for an extended, low excitation cold gas component
that implies that the total molecular gas mass in IRAS F10214+4724 is a factor
>~2 greater than that calculated using spatially unresolved CO observations.
