We present a DFT/classical molecular dynamics model of DNA charge conductivity. The model involves a temperature-driven, hole-hopping charge transfer and includes the time-dependent nonequilibrium interaction of DNA with its molecular environment. We validate our method against a variety of hole transport experiments. The method predicts a significant hole-transfer slowdown of similar to 35% from dry to wet DNA with and without electric field bias. In addition, in agreement with experiments, it also predicts an insulating behavior of (GC)(N) oligomers for 40 < N < 1000, depending on the experimental setup.