The potential applications of DNA either as template or as molecular wires make of crucial importance to understand the microscopic mechanism leading supporting (or hindering) charge migration through this molecule. The experimental studies give very striking results, which range from insulating up to superconducting behavior. Theoretically, it is very important to include dynamical effects, since DNA is known to be a very flexible molecule. The dynamical effects of the solvent should be taken into account. In this work, we study charge transport through short Poly(G)-Poly(C) DNA within a minimal tight binding model. The model parameters are extracted from snapshots along QM/MM trajectories via DFTB approximation and thus include internal and solvent dynamical effects. We perform a statistical analysis of the time-dependent onsite and electronic hopping and show a broad non symmetric distribution. Green function formalism is used to calculate the transport characteristics and demonstrate how the average quantities depend on the relation between system time scales.