A fundamental requirement for a molecule to be considered a molecular wire (MW) is the ability to transport electrical charge with a reasonably low resistance. We have carried out two experiments that measure first, the charge transfer from an electrode to the molecule, and second, the dielectric response of the MW. The latter experiment requires no contacts to either end of the molecule. From our experiments we conclude that adsorbed individual DNA molecules have a resistivity similar to mica, glass, and silicon oxide substrates. Therefore adsorbed DNA is not a conductor, and it should not be considered as a viable candidate for MW applications. Parallel studies on other nanowires, including single-walled carbon nanotubes, showed conductivity as expected.