Context. Minor mergers are important processes contributing significantly to how galaxies evolve across the age of the Universe. Their impact on the growth of supermassive black holes and star formation is profound – about half of the star formation activity in the local Universe is the result of minor mergers. Aims. The detailed study of dense molecular gas in galaxies provides an important test of the validity of the relation between star formation rate and HCN luminosity on different galactic scales – from whole galaxies to giant molecular clouds in their molecular gas-rich centers. Methods. We use observations of HCN and HCO⁺ 1−0 with NOEMA and of CO3−2 with the SMA to study the properties of the dense molecular gas in the Medusa merger (NGC 4194) at 1′′ resolution. In particular, we compare the distribution of these dense gas tracers with CO2−1 high-resolution maps in the Medusa merger. To characterize gas properties, we calculate the brightness temperature ratios between the three tracers and use them in conjunction with a non-local thermodynamic equilibrium (non-LTE) radiative line transfer model. Results. The gas represented by HCN and HCO⁺ 1−0, and CO3−2 does not occupy the same structures as the less dense gas associated with the lower-J CO emission. Interestingly, the only emission from dense gas is detected in a 200 pc region within the “Eye of the Medusa”, an asymmetric 500 pc off-nuclear concentration of molecular gas. Surprisingly, no HCN or HCO⁺ is detected for the extended starburst of the Medusa merger. Additionally, there are only small amounts of HCN or HCO⁺ associated with the active galactic nucleus. The CO3−2/2−1 brightness temperature ratio inside “the Eye” is ~2.5 – the highest ratio found so far – implying optically thin CO emission. The CO2−1/HCN 1−0 (~9.8) and CO2−1/HCO⁺ 1−0 (~7.9) ratios show that the dense gas filling factor must be relatively high in the central region, consistent with the elevated CO3−1/2−1 ratio. Conclusions. The line ratios reveal an extreme, fragmented molecular cloud population inside the Eye with large bulk temperatures (T > 300 K) and high gas densities (n(H₂) > 10⁴ cm^-3). This is very different from the cool, self-gravitating structures of giant molecular clouds normally found in the disks of galaxies. The Eye of the Medusa is found at an interface between a large-scale minor axis inflow and the central region of the Medusa. Hence, the extreme conditions inside the Eye may be the result of the radiative and mechanical feedback from a deeply embedded, young and massive super star cluster formed due to the gas pile-up at the intersection. Alternatively, shocks from the inflowing gas entering the central region of the Medusa may be strong enough to shock and fragment the gas. For both scenarios, however, it appears that the HCN and HCO⁺ dense gas tracers are not probing star formation, but instead a post-starburst and/or shocked ISM that is too hot and fragmented to form newstars. Thus, caution is advised in taking the detection of emission from dense gas tracers as evidence of ongoing or imminent star formation.