There are some interesting real-world examples of the forbidden experiment as described by Muke. Some children actually do grow up without language. "Wild Children", who grow up completely on their own, or are intentionally prevented from having any contact with people by neglectful parents, have no such exposure. However, their upbringing tends to traumatic in the extreme, making them poor subjects for any sort of research into natural language.
However, there is another interesting case, that of deaf children born to hearing parents. These children may grow up in a perfectly normal home environment, but because of their lack of exposure to either spoken language or signed language at a young age, have no "native language" at all.
What all of these cases point to, though, is not any mysterious primal language. What actually happens when children grow up without exposure to language is that the areas in their brains devoted to the production and comprehension of language never develop properly, and learning any language at all in later life may be difficult or even impossible, depending on the age at which they are first exposed to language. The critical age for natural language acquisition would seem to be around four years, with some individual variation.
Needless to say, this raises interesting Chicken-and-egg style problems for linguistic anthropologists. The current hypothesis is that humans evolved language through a series of gradual, iterative steps, meaning that there would be no "first language". Even if there were, there are some pretty severe logical flaws in the idea that a baby would know it.