Electronic transport through DNA wires in the presence of a strong dissipative environment is investigated. We show that new bath-induced electronic states are formed within the band gap. These states show up in the linear conductance spectrum as a temperature dependent background and lead to a crossover from tunneling to thermal activated behavior with increasing temperature. Depending on the strength of the electron-bath coupling, the conductance at the Fermi level can show a weak exponential or even an algebraic length dependence. Our results suggest a new environmentally induced transport mechanism. This might be relevant for the understanding of molecular conduction experiments in liquid solution, such as those recently performed on poly(GC) oligomers in a water buffer (B. Xu et al., Nano Lett. 4, 1105 (2004)).