Ok, I couldn't stay away from this for very long.
So Hannibal succeeds in sacking Rome, massacres the Senate, and sells a great deal of the Roman citizenry within Rome and surrounding colonae into slavery, with camps on the western coastline of Latium retaining native Latins and Romans while waiting for Phoenician and Greek merchant vessels to collect them. The warships of the Roman navy in dock are confiscated by Hannibal's forces. Within decades, central Italy or Latium, Etruria and Umbria, bereft of central authority, could be targeted for expansion by the Celts, Samnites, or from abroad.
If he captures Rome after 212 BCE, Hellenic city-state of Syracuse in Sicily would no longer be in any position to oppose Carthaginian expansionism on the island.
The Samnites in southern Italy might be able to revive their federation in the absence of Roman rule.
The Celtic tribes of the Boii and the Insubres would be able to dominate northern Italy.
Carthage's supremacy at sea may be restored within a few years of Rome's destruction. Although the hidebound oligarchy of Carthage may limit the long-term survival of the state. Scenarios abound where Hannibal may gather his forces, overthrow the Senate, Hundred and Four council, and install a new dynastic regime. But OTOH, since his family have been ruling the Iberian Punic territories since the time of his father, he might just establish a seperate Punic polity in the Mediterranean which forces Carthage to bow to its terms.
Another fate for Carthage could that its eventually overthrown by a growing confederation of Numidian tribes, whom may or may not capture Carthage and establish it as the capital of their new kingdom. In that TL, the Punic domains in Spain and Sicily would carry on as before, although Iberia could end being ruled in the future by growing Lusitanni or Celtiberian Arevaci forces.
In the absence of the Roman Republic, political entities in Gaul could take shape. The Arverni tribe, who are mentioned as leading the most impressive tribal confederation in Gaul until their defeat by Rome in the 120's BCE, would go from strengh to strengh, totally subsuming rivals like the Aedui, Sequani, Lemovicii, Allobroges, Aquitanni, the Volcae-Arecomici and the Belgae. Plus Greek colonies on Gauls southern coast such as Massalia (Marseille) could end up as a protectorate of whatever Gallic polity arises.
Certain conditions were needed for the spread of Christianity. With Rome cut down before its prime, there is no reason in my opinion that we would be seeing the same thing happen. The dominant religions in this TL could be derived from Celtic Polytheism, Greek Polytheism, and the Thraco-Dacian cult of Zalmoxis, which is believed to be a form of Monotheism.
The Phoenician religion may survive in North Africa, although if its true about the practice of infant blood sacrifices, hopefully it may have gradually become out-phased or even abolished as a religious practice.
Celtic Polytheism was guided and regulated by the Druidic class in society. They were an intertribal group whom occasionally assembled to revise the common body of religious-based laws that they all abided by. There is potential in this.