Romans weren’t around 3500 years ago and Rome could never have surrendered to Islam.
Rome fell in 476AD and Islam was founded around 610AD.
One of the most negative consequences of the contact between Islam and the Eastern Roman Empire was the Moslem adoption of a form of government popular among the Romans ~ the "emperor" or "dictator". Sharia law, right up to 1000 AD or thereabouts when "the book was closed" drew heavily from the worst elements of Eastern law.
To a considerable degree the Ottoman Empire and the Roman Empire had the same faults for the same reasons.
The Western Empire technically "fell" in the 400s, but that was simply a change in dynasty since the replacements sought to preserve the Western Empire.
The Dark Ages happened with a bang in the mid 500s and had NOTHING to do with wandering bands of savages!