Mass models of a sample of 171 low- and high-surface brightness galaxies are presented in the context of the cold dark matter (CDM) theory using the NFW dark matter halo density distribution to extract a new concentration-viral mass relation (c-M_vir_). The rotation curves (RCs) are calculated from the total baryonic matter based on the 3.6{mu}m-band surface photometry, the observed distribution of neutral hydrogen, and the dark halo, in which the three adjustable parameters are the stellar mass-to-light ratio, halo concentration, and virial mass. Although accounting for a NFW dark halo profile can explain RC observations, the implied c-M_vir_ relation from RC analysis strongly disagrees with that resulting from different cosmological simulations. Also, the M/L-colour correlation of the studied galaxies is inconsistent with that expected from stellar population synthesis models with different stellar initial mass functions. Moreover, we show that the best-fitting stellar M/L ratios of 51 galaxies (30 per cent of our sample) have unphysically negative values in the framework of the {Lambda}CDM theory. This can be interpreted as a serious crisis for this theory. This suggests either that the commonly used NFW halo profile, which is a natural result of {Lambda}CDM cosmological structure formation, is not an appropriate profile for the dark haloes of galaxies, or, new dark matter physics or alternative gravity models are needed to explain the rotational velocities of disc galaxies.