Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (HI) observations of 30 compact groups and define a new way to quantify the group HI content as the HI-to-stellar mass ratio of the group as a whole. We compare the HI content with mid-IR indicators of star formation and optical g-r color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in HI-poor groups, and galaxies with active star formation are more commonly found in HI-rich groups. Intriguingly, we also find "rogue" galaxies whose star formation does not correlate with group HI content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the HI. We speculate that this mismatch between mid-IR activity and HI content is a consequence of strong interactions in this environment that can strip HI from galaxies and abruptly affect star-formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier Universe.