  We present deep kpc- and pc-scale neutral atomic hydrogen (HI) absorption
observations of a very young radio source (< 5000 yrs), 4C 31.04, using the
WSRT and the Global VLBI array. Using $z=0.0598$, we detect a broad absorption
feature centred at the systemic velocity, and narrow absorption redshifted by
220 km/s both previously observed. Additionally, we detect a new blueshifted,
broad, shallow absorption wing. At pc scales, the broad absorption at the
systemic velocity is detected across the entire radio source while the shallow
wing is only seen against part of the eastern lobe. The velocity dispersion of
the gas is overall high ($\geq$40 km/s), and is highest (>60 km/s) in the
region including the outflow and the radio hot spot. While we detect a velocity
gradient along the western lobe and parts of the eastern lobe, most of the gas
along the rest of the eastern lobe exhibits no signs of rotation. We therefore
conclude that the radio lobes of 4C 31.04 are expanding into a circumnuclear
disc, partially disrupting it and making the gas highly turbulent. The
distribution of gas is predominantly smooth at the spatial resolution of ~4 pc
studied here. However, clumps of gas are also present, particularly along the
eastern lobe. This lobe is strongly interacting with the clouds and driving an
outflow ~35 pc from the radio core, with a mass-outflow rate of $0.3 \leq
\dot{M} \leq 1.4$ M$_\odot$/yr. We compare our observations with a model on the
survival of atomic gas clouds in radio-jet-driven outflows and find that the
existence of a sub-kpc outflow implies high gas density and inefficient mixing
of the cold gas with the hot medium, leading to shorter cooling times. Overall,
this provides further evidence of the strong impact of young radio jets on cold
ISM and supports the predictions of simulations regarding jet$-$ISM
interactions and the nature of the gas into which the jets expand.
