Please note: The above are the only authentic images of Roman Emperors available to the public. The Sassanians were very powerful, and had already captured a Roman Emperor. But the problem was that even as the Byzantine Emperors had to deal with the marauding Albinos, they were also constantly at war with the resurgent Persian Sassanian Kings, who wanted to reclaim their former territories in Anatolia and Europe. That left only Byzantium in Anatolia, as the only check against the Albinos marauding throughout Europe. And we also know that the White tribes went 'Hog-wild', conquering Roman territories even into North Africa.
But there is no doubt that the western Roman Empire fell, and the widespread and long-term social disarray and insecurity following the decline of the Roman Empire and the gradual affiliation of masses of people with military overlords who could protect them constitutes the big picture of medieval society in Europe. The eastern half became the Byzantine Empire, with its capital at Constantinople (modern Istanbul). Some say the split into an eastern and western empire governed by separate emperors caused Rome to fall. The 476 date for the Fall of Rome is conventionally acceptable because that's when the Germanic Odoacer deposed the last Roman emperor to rule the western part of the Roman Empire.