We present Very Large Array observations of the neutral hydrogen and radio continuum of NGC 34 (= NGC 17 = Mrk 938). This object is an ideal candidate for studying the fate of gas in mergers, since, as shown by an optical study done by Schweizer & Seitzer, it is a gas-rich ("wet") merger remnant of two disk galaxies of unequal mass hosting a strong central starburst and a weak active galactic nucleus (AGN). We detect H i emission from both tidal tails and from nearby galaxies, suggesting that NGC 34 is actually part of a gas-rich group and might have recently interacted with one of its companions. The kinematics of the gas suggests this remnant is forming an outer disk of neutral hydrogen from the gas of the northern tail. We also detect broad H i absorption (514 ± 21 km s −1 wide) at both negative and positive velocities with respect to the systemic velocity. This absorption could be explained by the motions of the tidal tails or by the presence of a circumnuclear disk. In addition, we present radio-continuum images that show both nuclear (62.4 ± 0.3 mJy) and extra-nuclear emission (26.5 ± 3.0 mJy). The extra-nuclear component is very diffuse and in the shape of two radio lobes, spanning 390 kpc overall. This emission could be a signature of an AGN that has turned off or it could originate from a starburst-driven superwind. We discuss the possible scenarios that explain our observations, and what they tell us about the location of the gas and the future evolution of NGC 34.