I've got an undergraduate degree in linguistics - which, granted, isn't much, but i did spend some time learning about language acquisition. The general consensus within linguistics is that there exists both a language acquisition device (LAD) and a critical period for language learning. Language learning is a biological process on par with learning how to process visual data that (in neurotypical individuals) unfolds regularly given adequate input. After somewhere between 11-13 years the LAD switches off, and languages that are learned after this critical period are typically learned imperfectly.
I've seen side-by-side fMRI scans of people speaking two languages they learned before the critical period and of people speaking a language learned before and a language learned after. In the true bilingual speakers, both languages lit up the same area of the brain, and in the speakers who learned a new language after the critical period, the post-critical language lit up a different area of the brain from the native language.
As far as post-critical-period second language acquisition goes, there is some indication that the LAD is involved in the process - there is a specific order in which English speakers will learn grammatical features of German regardless of who taught them or what method they used to learn the language. There are actually some language acquisition theorists (Krashen in particular) who think that language processing and production (at a grammatical level) is all done at an automatic level, and that all our conscious brains do is monitor what comes out.
The environment you learn the language in and your degree of identification with the target language's culture do play a pretty big role in how accurately you'll be able to reproduce the target language, though.
Also, programming "languages" aren't capital-L languages and are (presumably) not handled by the part of the brain that handles language.