We present [C II] and [O I] observations from Herschel and CO(1-0) maps from the Combined Array for{\dag} Research in Millimeter Astronomy (CARMA) of the Hickson Compact Group HCG 57, focusing on the galaxies HCG 57a and HCG 57d. HCG 57a has been previously shown to contain enhanced quantities of warm molecular hydrogen consistent with shock and/or turbulent heating. Our observations show that HCG 57d has strong [C II] emission compared to L$_{\rm FIR}$ and weak CO(1-0), while in HCG 57a, both the [C II] and CO(1-0) are strong. HCG 57a lies at the upper end of the normal distribution of [C II]/CO and [C II]/FIR ratios, and its far-IR cooling supports a low density warm diffuse gas that falls close to the boundary of acceptable PDR models. However, the power radiated in the [C II] and warm H$_2$ emission have similar magnitudes, as seen in other shock-dominated systems and predicted by recent models. We suggest that shock-heating of the [C II] is a viable alternative to photoelectric heating in violently disturbed diffuse gas. The existence of shocks is also consistent with peculiar CO kinematics in the galaxy, indicating highly non-circular motions are present. These kinematically disturbed CO regions also show evidence of suppressed star formation, falling a factor of 10-30 below normal galaxies on the Kennicutt-Schmidt relation. We suggest that the peculiar properties of both galaxies are consistent with a highly dissipative off-center collisional encounter between HCG 57d and 57a, creating ring-like morphologies in both systems. Highly dissipative gas-on-gas collisions may be more common in dense groups because of the likelihood of repeated multiple encounters. The possibility of shock-induced SF suppression may explain why a subset of these HCG galaxies have been found previously to fall in the mid-infrared green valley. ; Comment: ApJ accepted, 16 pages, 12 figures, 3 tables