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We analyze the effect of a pure distortion of nuclear potential on nonequilibrium-vibration-assisted tunneling through a molecular quantum dot with a single level coupled to the vibrational mode. In this study, we employ rate equations to examine the current-voltage characteristics and zero-frequency shot noise. We find that distortion induces a strong negative differential conductance (NDC) and a giant Fano factor for an anionic molecule; while a weak NDC and a nearly Poissonian shot noise occur for a neutral molecule. We discuss, in detail, the reasons for these asymmetric transport properties.