We present new HST NICMOS observations of NGC 4945, a starburst galaxy hosting a highly obscured active nucleus that is one of the brightest extragalactic sources at 100 keV. The HST data are complemented with ground based [Fe II] line and mid-IR observations. A 100pc-scale starburst ring is detected in Pa alpha, while H-2 traces the walls of a super bubble opened by supernova-driven winds. The conically shaped cavity is particularly prominent in Pa alpha equivalent width and in the Pa alpha/H-2 ratio. Continuum images are heavily affected by dust extinction and the nucleus of the galaxy is located in a highly reddened region with an elongated, disk-like morphology. No manifestation of the active nucleus is found, neither a strong point source nor dilution in CO stellar features, which are expected tracers of AGN activity Even if no AGN traces are detected in the near-IR, with the currently available data it is still not possible to establish whether the bolometric luminosity of the object is powered by the AGN or by the starburst: we demonstrate that the two scenarios constitute equally viable alternatives. However, the absence of any signature other than in the hard X-rays implies that, in both scenarios, the AGN is non-standard: if it dominates, it must be obscured in all directions, conversely, if the starburst dominates, the AGN must lack UV photons with respect to X-rays. An important conclusion is that powerful AGNs can be hidden even at mid-infrared wavelengths and, therefore, the nature of luminous dusty galaxies cannot be always characterized by long-wavelength data alone but must be complemented with sensitive hard X-ray observations.