We study the atomic (HI) and molecular hydrogen (H2) contents of early-type galaxies (ETGs) and their gas sources using the GALFORM model of galaxy formation. This model uses a self-consistent calculation of the star formation rate (SFR), which depends on the H2 content of galaxies. We first present a new analysis of HIPASS and ATLAS3D surveys, with special emphasis on ETGs. The model predicts HI and H2 contents of ETGs in agreement with the observations from these surveys only if partial ram pressure stripping of the hot gas is included, showing that observations of neutral gas in `quenched galaxies place stringent constraints on the treatment of the hot gas in satellites. We find that ~90% of ETGs at z=0 have neutral gas contents supplied by radiative cooling from their hot halos, 8% were supplied by gas accretion from minor mergers that took place in the last 1Gyr, while 2% were supplied by mass loss from old stars. The model predicts neutral gas fractions strongly decreasing with increasing bulge fraction. This is due to the impeded disk regeneration in ETGs, resulting from both active galactic nuclei feedback and environmental quenching by partial ram pressure stripping of the hot gas.