Compact groups of galaxies provide a unique environment locally for studying the mechanisms by which star formation occurs amid ongoing gravitational encounters. Compact groups are thus potentially the most relevant local analogues of early Universe galaxy and cluster formation and evolution. To catalogue star formation under these conditions, we present near and mid-infrared observations of a sample of 12 Hickson Compact Groups comprising 45 galaxies. We find evidence that galaxies in the most gas-rich groups are typically the most actively star-forming while those in the most gas-poor groups tend to be tightly clustered around a narrow range in colours consistent with the integrated light from a quiescent stellar population. We interpret these trends as indicating that galaxies in gas-rich groups experience star formation and/or nuclear activity until their neutral gas is consumed, stripped, or ionized. Surprisingly, the galaxies in this sample exhibit a ``gap'' between gas-rich and gas-poor groups in infrared colour space that is sparsely populated and not seen in other galaxy samples. We interpret this gap as indicating rapid evolution of galaxy properties in response to dynamical effects in the compact group environment.