As FYI, linguistic and cognitive research strongly support that the commonality in languages are not due (necessarily) to common linguistic ancestry, but rather to hard-wiring of the human brain. i.e., see Chomsky's research.
It is not so much that we all once spoke the same language, and therefore can learn other people's languages, as it is that language, being a uniquely human phenomenon, is intimately tied in its structural workings to that of the human brain.
We may have had a relatively unified form of communication at some point, however, since it is possible that people radiated out of Africa the first time (with H. erectus, unlikely to have had full language) but then did once again later (with modern H. sapiens, who may well have had full language). It's really difficult to figure out when language emerges in the human evolutionary lineage because the potential for a full range of sounds and the associated slight uneven development of the brain (left and right hemisphere) is extremely difficult to see in the fossil record, as it has to do with soft tissues, which don't preserve. The capacity for language has a lot to do with the placement of the hyoid bone and the soft tissue structures in the throat- chimps and other apes lack the capacity for linguistic virtuousity in part because the placement of their vocal cords and epiglottis high up in the throat. Incidentally, the upside of this for them is that choking hardly ever happens. Humans pay the price for linguistic virtuosity by a much higher risk of choking to death, especially as little kids learn to master breathing, swallowing, and making noise at the same time.
I tend to think the Tower of Babel story is useful in terms of meaning, but probably does not correspond to a literal global single language time period. Perhaps it corresponds to a literal Middle East single language time period, which would have encompassed the known world at the time and therefore be considered global by the folks who authored the story. Similar to the flood... a local but widespread event, misinterpreted as a global event, since it included everyone and everywhere that was known at the time.
