We present a theoretical analysis of the effects of the environment on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to static disorder and (ii) phonon-induced scattering of the carriers between the localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the I-V characteristics becomes wider. A simple physical explanation of this effect is provided.