Close, but not quite. The statue of Daniel 2 gives you the framework on which to build the prophecies of Daniel 7,8,11 and 12. The head of gold, Babylon. Defeated as you say by Meda-Persia, the silver chest and arms. They were defeated by Greece, bronze torso, (Alexander the Great), whose empire was divided eventually into 4 (see Daniel 7:6 and 8:8). Out of one of the compass points (Daniel 8:9) came a little horn, the pagan Roman empire, the iron legs, which grew into a powerful empire, not the same little horn one as in Daniel 7, which did indeed collapse and was taken over by 10 barbarian tribes, 7 of which became the principle nations of early Europe. The Roman empire however, the iron, although it changed by connecting itself to the clay, was still iron... Was still Rome... Until it was destroyed at the second coming. There was no gap or time when Rome didn't exist. There is no resurgence or revival of the pagan empire. Rome had never gone away.
So. The question is, where was it in history? The answer is, and the only answer, is found in the Roman Catholic Church. I know, they don't like to be called Roman. But that's what they are. They are Rome, only Rome, and all Rome.
Notice on Daniel 8 how the little horn grew to exceeding great power, to the south, to the east, and to the pleasant land? (Vs9), but that at some time in it's history it set it's sights on heavenly spiritual authorities and powers, to devour them as it had done to earthly powers. This became papal Rome, exalting itself even to challenge God by changing His laws. (Daniel 7:25)
Realize this... Rome isn't coming again, it's never left.