The basal ganglia complex has been implicated in many neurological processes but it is not functionally nor anatomically independent of the rest of the brain.

Parkinson's Disease has been directly linked to damage to the substantia nigra which is part of the basal ganglia complex. Similarly, Huntington's Disease has been directly linked to damage to the striatum which is also part of the basal ganglia complex.

I don't know of any other neurological disorders which have been directly linked to damage of any specific part of the basal ganglia complex.