  The merger remnant NGC 34 is a local luminous infrared galaxy (LIRG) hosting
a nuclear starburst and a hard X-ray source associated with a putative,
obscured Seyfert~2 nucleus. In this work, we use adaptive optics assisted near
infrared (NIR) integral field unit observations of this galaxy to map the
distribution and kinematics of the ionized and molecular gas in its inner
$\mathrm{1.2\,kpc \times 1.2\,kpc}$, with a spatial resolution of 70~pc. The
molecular and ionized gas kinematics is consistent with a disc with projected
major axis along a mean PA~=~$\mathrm{-9^{\circ}.2 \pm 0^{\circ}.9}$. Our main
findings are that NGC~34 hosts an AGN and that the nuclear starburst is
distributed in a circumnuclear star-formation ring with inner and outer radii
of $\approx$~60 and 180~pc, respectively, as revealed by maps of the
$\mathrm{[Fe II] / Pa\beta}$ and $\mathrm{H_{2} / Br\gamma}$ emission-line
ratios, and corroborated by PCA Tomography analysis. The spatially resolved NIR
diagnostic diagram of NGC~34 also identifies a circumnuclear structure
dominated by processes related to the stellar radiation field and a nuclear
region where $[Fe II]$ and H$_2$ emissions are enhanced relative to the
hydrogen recombination lines. We estimate that the nuclear X-ray source can
account for the central H$_2$ enhancement and conclude that $[Fe II]$ and H$_2$
emissions are due to a combination of photo-ionization by young stars,
excitation by X-rays produced by the AGN and shocks. These emission lines show
nuclear, broad, blue-shifted components that can be interpreted as nuclear
outflows driven by the AGN.
