Compact group galaxies often appear unaffected by their unusually dense environment. Closer examination can, however, reveal the subtle, cumulative effects of multiple galaxy interactions. Hickson Compact Group (HCG) 59 is an excellent example of this situation. We present a photometric study of this group in the optical (HST), infrared (Spitzer) and X-ray (Chandra) regimes aimed at characterizing the star formation and nuclear activity in its constituent galaxies and intra-group medium. We associate five dwarf galaxies with the group and update the velocity dispersion, leading to an increase in the dynamical mass of the group of up to a factor of 10 (to 2.8e13 Msun), and a subsequent revision of its evolutionary stage. Star formation is proceeding at a level consistent with the morphological types of the four main galaxies, of which two are star-forming and the other two quiescent. Unlike in some other compact groups, star-forming complexes across HCG 59 closely follow mass-radius scaling relations typical of nearby galaxies. In contrast, the ancient globular cluster populations in galaxies HCG 59A and B show intriguing irregularities, and two extragalactic HII regions are found just west of B. We age-date a faint stellar stream in the intra-group medium at ~1 Gyr to examine recent interactions. We detect a likely low-luminosity AGN in HCG 59A by its ~10e40 erg/s X-ray emission; the active nucleus rather than star formation can account for the UV+IR SED. We discuss the implications of our findings in the context of galaxy evolution in dense environments.