So, w.r.t to Pitt's research, proving that the brain could compute anything (like a Turing machine) does not help in understanding how it does one particular thing, for e.g. language?
Kind of. It's not the idea that the brain is a Turing machine that's the problem -- I think it's fairly well established that given enough scratch paper, a human _could_ manually execute an algorithm for any computable function. The problem is more specifically that in Pitt's model, all of the behavioral work is offloaded to the abstract logic, leaving none for the physical wetware. Of course, today we know that the brain does have quite a bit of physical structure, and we have learned a lot about how the brain functions by looking at these structures.