  A new method is used to measure the physical conditions of the gas in damped
Lyman-alpha systems (DLAs). Using high resolution absorption spectra of a
sample of 80 DLAs, we are able to measure the ratio of the upper to lower
fine-structure levels of the ground state of C II and Si II. These ratios are
determined solely by the physical conditions of the gas. We explore the allowed
physical parameter space using a Monte Carlo Markov Chain method to constrain
simultaneously the temperature, neutral hydrogen density, and electron density
of each DLA. The results indicate that at least 5 % of all DLAs have the bulk
of their gas in a dense, cold phase with typical densities of ~100 cm-3 and
temperatures below 500 K. We further find that the typical pressure of DLAs in
our sample is log(P/k) = 3.4 [K cm-3], which is comparable to the pressure of
the local interstellar medium (ISM), and that the components containing the
bulk of the neutral gas can be quite small with absorption sizes as small as a
few parsec. We show that the majority of the systems are consistent with having
densities significantly higher than expected from a purely canonical WNM,
indicating that significant quantities of dense gas (i.e. n_H > 0.1 cm-3) are
required to match observations. Finally, we identify 8 systems with positive
detections of Si II*. These systems have pressures (P/k) in excess of 20000 K
cm-3, which suggest that these systems tag a highly turbulent ISM in young,
star-forming galaxies.
