Turbulent motion driven by the magnetorotational instability (MRI) is believed to provide an anomalous viscosity strong enough to account for observed accretion rates in protostellar accretion discs. In the first of two papers, we perform large-scale, three fluid simulations of a weakly ionized accretion disc and examine the linear and non-linear development of the MRI in the net-flux and zero net-flux cases. This numerical study is carried out using the multifluid magnetohydrodynamic code hydra. We examine the role of non-ideal effects, including ambipolar diffusion, the Hall effect and parallel resistivity, on the non-linear evolution of the MRI in weakly ionized protostellar discs in the region where the Hall effect is believed to dominate. We find that angular momentum transport, parametrized by the α-parameter, is enhanced by inclusion of non-ideal effects in the parameter space of the disc model. The case where Ω {dot operator} B is negative is explored and the Hall effect is shown to have a stabilizing influence on the disc in this case. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.