DNA naturally exists in a solvent environment, comprising water and salt molecules such as sodium, potassium, magnesium, etc. Along with the sequence, the solvent conditions become a vital factor determining DNA structure and thus its conductance. Over the last two decades, researchers have measured DNA conductivity both in hydrated and almost dry (dehydrated) conditions. However, due to experimental limitations (the precise control of the environment), it is very difficult to analyze the conductance results in terms of individual contributions of the environment. Therefore, modeling studies can help us to gain a valuable understanding of various factors playing a role in charge transport phenomena. DNA naturally has negative charges located at the phosphate groups in the backbone, which provides both the connections between the base pairs and the structural support for the double helix. Positively charged ions such as the sodium ion (Na^{+}), one of the most commonly used counterions, balance the negative charges at the backbone. This modeling study investigates the role of counterions both with and without the solvent (water) environment in charge transport through double-stranded DNA. Our computational experiments show that in dry DNA, the presence of counterions affects electron transmission at the lowest unoccupied molecular orbital energies. However, in solution, the counterions have a negligible role in transmission. Using the polarizable continuum model calculations, we demonstrate that the transmission is significantly higher at both the highest occupied and lowest unoccupied molecular orbital energies in a water environment as opposed to in a dry one. Moreover, calculations also show that the energy levels of neighboring bases are more closely aligned to ease electron flow in the solution.