As a proponent of biolinguistics, my bet is that as we study those neural substrates more closely, we'll probably just learn more about the sensorimotor systems (which we largely share in common with other mammals) that have been coopted for expression of language in humans.

We already have a useful pathway for investigation: data from speech/sign of a speaker of a particular language. In fact this already yields a kind of overabundance of data. The tricky part is finding the right kind of data via careful experimentation and organising it, by building explanatory theories of language that meet the conditions of evolvability and learnability.

(Which is not to say that cognitive sciences can't shed any light on this, but studying the brain independently of linguistic experimentation is a dead end IMO. Brain imaging studies coupled with linguistic studies have yielded interesting results - see Andrea Moro's work on "impossible languages").