I wouldn't say that Rome was necessarily doomed by the time of Marius, but the roots of what brought it down were definitely sown in the political changes in the first century BC.

I would say that the Crisis of the Third Century, though, was when the empire started to go downhill. But still, Diocletian and his successors were able to hold it together, so I would not say it was necessarily doomed yet. As people have pointed out, once the Vandals took North Africa, the Western Empire was in real trouble, as that was the main source of grain.

However, I think even up to Justinian, the idea of a Roman Empire was still viable. The reconquest of the Empire was intially very successful. And even before that, the Vandals, Goths, Franks, ect. were very willing to become Romanized, and adopted Roman culture, language, law, ect. So if things turned out differently, I could see a Mediterranean world governed by the Byzantines, with "barbarian" Romanized states on its fringes. However, the force that really doomed the idea of a Roman Empire was Islam. It swept through the Byzantine Empire, took Egypt (the other main source of grain), North Africa, and Spain. And most importantly, the regions conquered by the Arabs rapidly abandoned the use of Greek (or, in the West, Latin) and the age-old Mediterranean culture in favor of the new, Arab culture. From then on, the culture makeup of the Medierranean changed, and even the Byzantine Empire, at least in my opinion, changed fundamentally and stopped being truly “Roman” so Roman civilization was essentially dead.

But my favorite reason for Rome’s fall is Voltaire’s: “This empire fell because it existed. Everything has to fall”