(From cond-mat/0506552): We calculate the non-linear tunneling current through a molecule with two electron-accepting orbitals which interact with an intramolecular vibration. We investigate the interplay between Coulomb blockade and non-equilibrium vibration-assisted tunneling under the following assumptions: (i) The Coulomb charging effect restricts the number of extra electrons to one. (ii) The orbitals are non-degenerate and couple asymmetrically to the vibration. (iii) The tunneling induces a non-equilibrium vibrational distribution; we compare with the opposite limit of strong relaxation of the vibration due to some dissipative environment. We find that a non-equilibrium feedback mechanism in the tunneling transitions generates strong negative differential conductance (NDC) in the model with two competing orbitals, whereas in a one-orbital model it leads only to weak NDC. In addition, we find another mechanism leading to weak NDC over a broader range of applied voltages. This pervasive effect is completely robust against strong relaxation of the vibrational energy. Importantly, the modulation of the electronic transport is based on an intramolecular asymmetry. We show that one can infer a non-equilibrium vibrational distribution when finding NDC under distinct gate- and bias-voltage conditions. In contrast, we demonstrate that any NDC effect in the one-orbital case is completely suppressed in the strong relaxation limit.