Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance parameters with the help of a discretized log-likelihood of the continuous process in the case of fully observed data. We discuss the difficulties generated by the hypoellipticity and provide a proof of the consistency of the estimator. We test our approach numerically on the hypoelliptic FitzHugh-Nagumo model, which describes the firing mechanism of a neuron.