Abridged: The small-- and intermediate--scale structure and the fraction of the ISM ionized by non--radiative processes is investigated in a small sample of four local starburst galaxies, imaged with the HST WFPC2. The sample comprises three dwarf galaxies, NGC3077, NGC4214, and NGC5253, and one giant spiral, NGC5236 (M83). The galaxies span a range in metallicity, luminosity, and environment, enabling the investigation of non--radiative ionization processes in a variety of galactic conditions. For this purpose, the four galaxies were imaged in the lines of H-beta(4861 A), [OIII](5007 A), H-alpha(6563 A), and [SII](6717,6731 A). The non--photoionized gas in these galaxies has been traced on scales ranging from a few tens of pc to a few hundred pc, providing a full budget for this ionized gas component. Using the `maximum starburst line' of Kewley et al. (2001) to discriminate between photoionized and non--photoionized gas, we find that in all four galaxies non--photoionization processes are responsible for a small fraction of the total H-alpha emission, at the level of 3%--4%. The starbursts in the three dwarf galaxies deposit a significant fraction, 70%-100%, of their mechanical energy into the surrounding interstellar medium and require time--extended (a few x 10^7 yr to ~10^8 yr) star formation, in order to account for the observed luminosity of the non--photoionized gas. In the massive spiral, the non--photoionized gas is concentrated in localized areas surrounded by active star--formation, with no evidence for extended structures (as those in the dwarfs). This confirms the picture that starbursts remain confined events in massive galaxies, likely due to the deep potential well.