We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semiquantitative model for the pi electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a "blocking" state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.