On the computational basis of a neurodynamical cortical model, we investigate a specific top-down visual cognitive impairment in brain-damaged patients known as visual spatial neglect. The computational cortical model accounts the neurodynamics underlying selective visual attention, is based on the "biased competition hypothesis" and structured in several network modules which can be related with the different areas of the dorsal and ventral path of the visual cortex. Spatial and object attention are accomplished by a multiplicative gain control that emerges dynamically through intercortical mutual biased coupling. By damaging the model in different ways, a variety of dysfunctions associated with visual neglect can be simulated and explained as disruption of specific subsystems. Essentially, the damage destabilizes the underlying intra- and intermodular mutually biased neurodynamical competition that macroscopically yields the functional deficits observed in visual neglect patients. In particular, we are able to explain the asymmetrical effect of spatial cueing on neglect, and the phenomenon of extinction in the framework of visual search.