Neuronal cell dysfunction plays an important role in neurodegenerative diseases. Oxidative stress can disrupt the redox balance within neuronal cells and may cause neuronal nitric oxide synthase (nNOS) to uncouple, contributing to the neurodegenerative processes. Experimental studies and clinical trials using nNOS cofactor tetrahydrobiopterin (BH4) and antioxidants in neuronal cell dysfunction have shown inconsistent results. A better mechanistic understanding of complex interactions of nNOS activity and oxidative stress in neuronal cell dysfunction is needed. In this study, we developed a computational model of neuronal cell using nNOS biochemical pathways to explore several key mechanisms that are known to influence neuronal cell redox homeostasis. We studied the effects of oxidative stress and BH4 synthesis on nNOS nitric oxide production and biopterin ratio (BH4/total biopterin). Results showed that nNOS remained coupled and maintained nitric oxide production for oxidative stress levels less than 230 nM/s. The results showed that neuronal oxidative stress above 230 nM/s increased the degree of nNOS uncoupling and introduced instability in the nitric oxide production. The nitric oxide production did not change irrespective of initial biopterin ratio of 0.05–0.99 for a given oxidative stress. Oxidative stress resulted in significant reduction in BH4 levels even when nitric oxide production was not affected. Enhancing BH4 synthesis or supplementation improved nNOS coupling, however the degree of improvement was determined by the levels of oxidative stress and BH4 synthesis. The results of our mechanistic analysis indicate that there is a potential for significant improvement in neuronal dysfunction by simultaneously increasing BH4 levels and reducing cellular oxidative stress.