That's completely incorrect. Yes, the Romans were defeated, but the Italians were not wiped by any means. Latin was the primary language being spoken on the Italian peninsula, and in Spain, and in much of France when the Romans were defeated.
Unfortunately, once the Roman Empire was defeated, communications between the regions broke down seriously. Romans had built roads. Romans had created an active empire in which there was plenty of trade. Once that was gone...people were separated. Having lived in Italy myself, I can see the effects of this. People became isolated, and when that happens, dialects begin to form.
When the Romans fell, dialects actually already existed...but they weren't prominent because there was a grand empire holding everything together. The fall of the Romans was a catalyst for the dialects to continue evolving. In Italy alone there are about 30 different dialects...and nobody really spoke the same language again until the late 1800s. The same thing happened in Spain and France.
Latin was still the language for the educated...but honestly...how many people were actually educated back in that time period? Thus, Latin as a world language began to falter, but remained a world language for the educated people. It remained like this until the 1700s and 1800s.
At this time, there was a rise of the middle class, and world trade as well. The British Empire had colonies all over the world (first in the Americas, and then in the Africas, and then in Asia as well...going into the 1900s). Because of the globality of the British Empire, English was the language of the trading world.
This caused the rise of English as a global language, and the final decline of Latin - even though Latin is still pervasive in all parts of society.
As far as English being the "language of the Gods" (quoted by @nthony), I think that that is completely false.
