(covers information from several alternate timelines)
The cerebral cortex was the part of the brain involved in many higher level tasks such as language, memory, and consciousness. The cerebral cortex includes the parietal lobes, the occipital lobe, the frontal lobe, and the temporal lobes.
A burst of seventy millivolts would burn out the cerebral cortex of a normal humanoid brain. This, however, could be cheated with an injection of an inoprovaline drug, which provided additional resistance against such excessive electro-stimulation. (DS9: "Life Support")
When Deanna Troi temporarily lost her empathic sense due to the influence of two-dimensional lifeforms in 2367, Dr. Crusher recorded a pattern of unresponsive neural cells in her cerebral cortex and cerebellum. (TNG: "The Loss")
In an alternate 2372, Harry Kim suggested disproving Strickler's accusation of espionage by running a microcellular scan of his cerebral cortex to prove his memory had not been altered. (VOY: "Non Sequitur")
Seven of Nine's cerebral cortex underwent severe stress in 2375, when a malfunctioning Borg vinculum caused numerous neural patterns from assimilated individuals to overwhelm her mind. (VOY: "Infinite Regress")
Later that year, Seven detected unusual synaptic activity in Kim's cerebral cortex. This was as a result of the biochemical bond created with Derran Tal during their intimate relationship. (VOY: "The Disease")