Even in the absence of sensory inputs, cortical and thalamic neurons can show structured patterns of ongoing spontaneous activity, whose origins and functional significance are not well understood. We use computer simulations to explore the conditions under which spontaneous activity emerges from a simplified model of multiple interconnected thalamocortical columns linked by long-range, top-down excitatory axons, and to examine its interactions with stimulus-induced activation. Simulations help characterize two main states of activity. First, spontaneous gamma-band oscillations emerge at a precise threshold controlled by ascending neuromodulator systems. Second, within a spontaneously active network, we observe the sudden "ignition" of one out of many possible coherent states of high-level activity amidst cortical neurons with long-distance projections. During such an ignited state, spontaneous activity can block external sensory processing. We relate those properties to experimental observations on the neural bases of endogenous states of consciousness, and particularly the blocking of access to consciousness that occurs in the psychophysical phenomenon of "inattentional blindness," in which normal subjects intensely engaged in mental activity fail to notice salient but irrelevant sensory stimuli. Although highly simplified, the generic properties of a minimal network may help clarify some of the basic cerebral phenomena underlying the autonomy of consciousness.