Silicon nanocrystals (Si NCs) have shown great promise for electroluminescent and photoluminescent applications. In order to optimize the properties of Si NC devices, however, electronic transport in Si NC films needs to be thoroughly understood. Here we present a systematic study of the temperature and electric field dependence of conductivity in films of alkyl-ligand-terminated Si NCs, which to date have shown the highest potential for device applications. Our measurements suggest that the conductivity is limited by the ionization of rare NCs containing donor impurities. At low bias, this ionization is thermally activated, with an ionization energy equal to twice the NC charging energy. As the bias is increased, the ionization energy is reduced by the electric field, as determined by the Poole-Frenkel effect. At large bias and sufficiently low temperature, we observe cold ionization of electrons from donor-containing NCs, with a characteristic tunneling length of about 1 nm. The temperature- and electric-field-dependent conductance measurements presented here provide a systematic and comprehensive picture for electron transport in lightly doped nanocrystal films.