Which theorist believed that language development begins with babbling, and that children learn grammatical uses of words because others do not respond to ungrammatical language?

The answer is: Noam Chomsky.

Explanation:

Chomsky has the belief, that we are born with predisposition to learn language; he also proposed ideas that were new ways of thinking about language, basically and one of them was exactly this one that you've mentioned in your question. He believed that is was quite a coincidence that humans on their majority, follow similar rules in grammar.