  We present an analysis of the molecular and atomic gas emission in the
rest-frame far-infrared and sub-millimetre, from the lensed z=2.3
sub-millimetre galaxy SMM J2135-0102. We obtain very high signal-to-noise
detections of 11 transitions from 3 species and limits on a further 20
transitions from 9 species. We use the 12CO, [CI] and HCN line strengths to
investigate the gas mass, kinematic structure and interstellar medium (ISM)
chemistry, and find strong evidence for a two-phase medium comprising a hot,
dense, luminous component and an underlying extended cool, low-excitation
massive component. Employing photo-dissociation region models we show that on
average the molecular gas is exposed to a UV radiation field that is ~1000 x
more intense than the Milky Way, with star-forming regions having a
characteristic density of n~10^4 /cm^3. These conditions are similar to those
found in local ULIRGs and in the central regions of typical starburst galaxies,
even though the star formation rate is far higher in this system. The 12CO
spectral line energy distribution and line profiles give strong evidence that
the system comprises multiple kinematic components with different conditions,
including temperature, and line ratios suggestive of high cosmic ray flux
within clouds. We show that, when integrated over the galaxy, the gas and
star-formation surface densities appear to follow the Kennicutt-Schmidt
relation, although when compared to high-resolution sub-mm imaging, our data
suggest that this relation breaks down on scales of <100pc. By virtue of the
lens amplification, these observations uncover a wealth of information on the
star formation and ISM at z~2.3 at a level of detail that has only recently
become possible at z<0.1, and show the potential physical properties that will
be studied in unlensed galaxies when ALMA is in full operation. (Abridged).
