Actually, IMHO allowing the Huns and other barbarians take up residence inside the borders of the empire was responsible for the fall of Rome. But we would never allow something like that to happen./sarc
They grew fat and lazy and started to consume meals at McCaesars!
That may have destroyed the EMPIRE....but what destroyed the REPUBLIC was resorting to extra legal means to change power. Sulla, Brutus and Caesar destroyed the Republic way before the Barbarians came in.
Rome never fell. It just shifted east to Constantinople, taking all the brains and money with it.