The blinking behavior of single Atto565 molecules on a glass surface is studied under air or nitrogen atmospheres using confocal microscopy. The broad distributions for both on- and off-time durations obey power law kinetics that are rationalized using a charge tunneling model. In this case, a charge is transferred from the Atto565 molecule to localized states found on the glass surface. Subsequent charge recombination by back charge tunneling from trap to Atto565 cation (i.e., dark state) restores the fluorescence. The off-time distribution is independent of excitation intensity (I), whereas the on-time distribution exhibits a power law exponent that varies with I. Two pathways have been identified to lead to the formation of the radical dark state. The first involves direct charge tunneling from the excited singlet S1 state to charge traps in the surrounding matrix, and the second requires charge ejection from the triplet T1 state after intersystem crossing from S1. Monte Carlo simulation studies complement the two-pathway model. Photobleaching curves of both single and ensemble molecules do not exhibit monoexponential decays suggesting complex bleaching dynamics arising from triplet and radical states.