The key is the word "deep" in deep learning. Someone (forgot ref) in the 80s proved that all non-linear functions could be approximated by a *single* layer neural network with, of course, a sufficiently large number of hidden units. I think this result probably discouraged people from seeking deeper network in the earlier era. 

But depth of the network is what proved to be the crucial element in hierarchical representation that drives the success of many of today's applications.