Studying the molecular component of the interstellar medium in metal-poor galaxies has been challenging because of the faintness of carbon monoxide emission, the most common proxy of H2. Here we present new detections of molecular gas at low metallicities, and assess the physical conditions in the gas through various CO transitions for 8 galaxies. For one, NGC 1140 (Z/Zsun ~ 0.3), two detections of 13CO isotopologues and atomic carbon, CI, and an upper limit for HCN(1-0) are also reported. After correcting to a common beam size, we compared 12CO(2-1)/12CO(1-0) (R21) and 12CO(3-2)/12CO(1-0) (R31) line ratios of our sample with galaxies from the literature and find that only NGC 1140 shows extreme values (R21 ~ R31 ~ 2). Fitting physical models to the 12CO and 13CO emission in NGC 1140 suggests that the molecular gas is cool (kinetic temperature Tkin<=20 K), dense (H2 volume density nH2 >= $106$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$), with moderate CO column density (NCO ~ $1016$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$) and low filling factor. Surprisingly, the [12CO]/[13CO] abundance ratio in NGC 1140 is very low (~ 8-20), lower even than the value of 24 found in the Galactic Center. The young age of the starburst in NGC 1140 precludes 13C enrichment from evolved intermediate-mass stars; instead we attribute the low ratio to charge-exchange reactions and fractionation, because of the enhanced efficiency of these processes in cool gas at moderate column densities. Fitting physical models to 12CO and CI emission in NGC 1140 gives an unusually low [12CO]/[12C] abundance ratio, suggesting that in this galaxy atomic carbon is at least 10 times more abundant than 12CO.