The basal ganglia (BG) represent a critical center of the nervous system for sensorial discrimination. Although it is known that Huntington’s disease (HD) affects this brain area, it still remains unclear how HD patients achieve paradoxical improvement in sensorial discrimination tasks. This paper presents a computational model of the BG including the main nuclei and the typical firing properties of their neurons. The BG model has been embedded within an auditory signal detection task. We have emulated the effect that the altered levels of dopamine and the degree of HD affectation have in information processing at different layers of the BG, and how these aspects shape transient and steady states differently throughout the selection task. By extracting the independent components of the BG activity at different populations, it is evidenced that early and medium stages of HD affectation may enhance transient activity in the striatum and the substantia nigra pars reticulata. These results represent a possible explanation for the paradoxical improvement that HD patients present in discrimination task performance. Thus, this paper provides a novel understanding on how the fast dynamics of the BG network at different layers interact and enable transient states to emerge throughout the successive neuron populations.