Transport through molecular devices with weak tunnel coupling to the leads but with strong coupling to a single vibrational mode is considered in the case where the vibration is damped by coupling to the environment. In particular, we investigate what influence the electrostatic coupling of the charge on the molecule to the vibrational modes of the environment has on the I-V characteristics. We find that, for comparable characteristic length scales of the van der Waals and electrostatic interaction of the molecule with the environmental vibrational modes, the I-V characteristics are qualitatively changed from what one would expect from orthogonality catastrophe and develop a steplike discontinuity at the onset of conduction. For the case of very different length scales, we recover dissipation consistent with modeling the electrostatic forces as an external influence on the system comprised of molecule and substrate, which implies the appearance of orthogonality catastrophe, in accord with previous results.