Although I think the information age and the computer metaphor played a significant role in the development of cognitive psychology, and the fall of behaviorism created an opportunity for new ways of thinking, it was neuroscience and artificial intelligence that lead to a clearer understanding of how the brain functioned and its relationship to behavior. According to Willingham (2007), neuroscientists became better able to provide tangible evidence as to how the mind could be studied in a scientific manner. (Behaviorists believed that only studying behavior was scientific.) A more definitive link between brain structure and function became apparent from examining brain-damaged individuals and associating the damaged area to the specific cognitive problem exhibited by the individual (Willingham 2007).
For example, the famous patient H.M. was studied after surgery to lessen his epileptic seizure activity, caused damage to areas that enable new memories (Willingham, 2007). Information from the studies of H.M.'s memory helped science develop theories as to how and by which brain structures memory works. H.M.'s long-term memory was intact, although he could not create new memories. Scientists could understand which structures were and were not essential in the type of memory still intact in H.M. Willingham (2007) makes the point that it was important to be able to use abstract constructs, such as H.M.'s intact (or primary) memory, to determine a link between structures and memory capabilities. Despite the fact that his hippocampus and other structures were damaged in the surgery, his primary and long-term memory still worked, so this knowledge illuminated which structures did play a possible role in the memory that no longer functioned in H.M.
Behaviorists were not fond of using abstract ideas such as memory because they couldn't be observed, but human studies, such as the case of H.M., helped to strengthen the significance of immeasurable functions and define stronger links between brain structures and their functions.
Willingham, D. T. (2007). Cognition: The thinking animal (3rd ed.). Upper Saddle River, NJ: Pearson/Allyn & Bacon.