(abridged) We present new Spitzer, UKIRT and MMT observations of the blue compact dwarf galaxy (BCD) Mrk 996, with an oxygen abundance of 12+log(O/H)=8.0. This galaxy has the peculiarity of possessing an extraordinarily dense nuclear star-forming region, with a central density of ~10^6 cm^{-3}. The nuclear region of Mrk 996 is characterized by several unusual properties: a very red color J-K = 1.8, broad and narrow emission-line components, and ionizing radiation as hard as 54.9 eV, as implied by the presence of the OIV 25.89 micron line. The nucleus is located within an exponential disk with colors consistent with a single stellar population of age >1 Gyr. The infrared morphology of Mrk 996 changes with wavelength. The IRS spectrum shows strong narrow Polycyclic Aromatic Hydrocarbon (PAH) emission, with narrow line widths and equivalent widths that are high for the metallicity of Mrk 996. Gaseous nebular fine-structure lines are also seen. A CLOUDY model requires that they originate in two distinct HII regions: a very dense HII region of radius ~580 pc with densities declining from ~10^6 at the center to a few hundreds cm^{-3} at the outer radius, where most of the optical lines arise; and a HII region with a density of ~300 cm^{-3} that is hidden in the optical but seen in the MIR. We suggest that the infrared lines arise mainly in the optically obscured HII region while they are strongly suppressed by collisional deexcitation in the optically visible one. The hard ionizing radiation needed to account for the OIV 25.89 micron line is most likely due to fast radiative shocks propagating in an interstellar medium. A hidden population of Wolf-Rayet stars of type WNE-w or a hidden AGN as sources of hard ionizing radiation are less likely possibilities.
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