The passage of a current through a solid requires a pathway for the movement of electrons or holes. A new class of phenalenyl-based neutral radical molecular conductors has recently been reported; a distinctive feature of these molecular solids is the absence of any obvious conducting pathway(s). These radicals do not stack in the solid state, and the requisite carbon-carbon contacts are all larger than the sum of the van der Waals distances. Magnetic susceptibility measurements show that the first compound to be isolated behaves as a free radical with one spin per molecule, apparently supporting the idea that there is little interaction between the molecules in the solid state. Nevertheless, this radical shows the highest conductivity (sigma(RT) = 0.05 S/cm), of any neutral organic solid, and the conduction mechanism is presently unresolved. In the present study, we report a structurally related radical with a resistivity 4 orders of magnitude higher than that of the previously reported radicals. We analyze the crystallographic and electronic structure of these solids in detail and argue that a conducting pathway is operative in many of these neutral radicals. We show that the very weak orbital overlap between well-spaced neighbors is sufficient to provide a conducting pathway in carbon-based free radicals providing that the pi-systems are not perpendicular, and we further argue that such effects may be operative in other organic molecules.