  We present explicit kinetic equations for quantum transport through a general
molecular quantum-dot, accounting for all contributions up to 4th order
perturbation theory in the tunneling Hamiltonian and the complete molecular
density matrix. Such a full treatment describes not only sequential,
cotunneling and pair tunneling, but also contains terms contributing to
renormalization of the molecular resonances as well as their broadening. Due to
the latter all terms in the perturbation expansion are automatically
well-defined for any set of system parameters, no divergences occur and no
by-hand regularization is required. Additionally we show that, in contrast to
2nd order perturbation theory, in 4th order it is essential to account for
quantum coherence between non-degenerate states, entering the theory through
the non-diagonal elements of the density matrix. As a first application, we
study a single-molecule transistor coupled to a localized vibrational mode
(Anderson-Holstein model). We find that cotunneling-assisted sequential
tunneling processes involving the vibration give rise to current peaks i.e.
negative differential conductance in the Coulomb-blockade regime. Such peaks
occur in the cross-over to strong electron-vibration coupling, where inelastic
cotunneling competes with Franck-Condon suppressed sequential tunneling, and
thereby indicate the strength of the electron-vibration coupling. The peaks
depend sensitively on the coupling to a dissipative bath, thus providing also
an experimental probe of the Q-factor of the vibrational motion.
