The potential applications of DNA oligomers in molecular electronics makes of crucial importance to understand the microscopic mechanisms of charge migration. Experimental studies provide very striking results, which range from insulating to superconducting behavior. Theoretically, it is very important to take into account dynamical effects, since DNA is known to be a flexible molecule. In this work, we study charge transport through short Poly(G)-Poly(C) molecules within a minimal tight binding Hamiltonian model. The model parameters are extracted from snapshots along molecular dynamic trajectories and thus effectively include internal and external (soventmediated) dynamical effects. We perform a statistical analysis of the time-dependent onsite energies and electronic hopping integrals and show that they can be fitted to Gaussian functions. We use Greens function techniques in order to calculate the linear conductance and the current-voltage characteristics and demonstrate how the average quantities do depend on the charge tunneling time.