We present a computational model of a thalamocortical relay neuron for exploring basal ganglia thalamocortical loop behavior in relation to Parkinson's disease and deep brain stimulation (DBS). Previous microelectrode, single-unit recording studies demonstrated that oscillatory interaction within and between basal ganglia nuclei is very often accompanied by synchronization at Parkinsonian rest tremor frequencies (3-10 Hz). These oscillations have a profound influence on thalamic projections and impair the thalamic relaying of cortical input by generating rebound action potentials. Our model describes convergent inhibitory input received from basal ganglia by the thalamocortical cells based on characteristics of normal activity, and/or low-frequency oscillations (activity associated with Parkinson's disease). In addition to simulated input, we also used microelectrode recordings as inputs for the model. In the resting state, and without additional sensorimotor input, pathological rebound activity is generated for even mild Parkinsonian input. We have found a specific stimulation window of amplitudes and frequencies for periodic input, which corresponds to high-frequency DBS, and which also suppresses rebound activity for mild and even more prominent Parkinsonian input. When low-frequency pathological rebound activity disables the thalamocortical cell's ability to relay excitatory cortical input, a stimulation signal with parameter settings corresponding to our stimulation window can restore the thalamocortical cell's relay functionality.