WI Marcellus Fails to Capture Syracuse

[Foxfire]

Prior to the Second Punic War, Syracuse was considered to be invulnerable; it had a reputation for the best anti-siege defenses in the Mediterranean, and Archimedes on the job to make them even better.
But, worried about Carthage using Sicily as a base from which to resupply their armies in Italy, Rome attacked it anyway, and eventually sacked the city.
So, first, how could we prevent Marcellus from successfully taking Syracuse, and second, how would that effect the rest of the war?

In OTL...
216 B.C.: Rome pulls its troops out of Sicily and replaces them with the disgraced survivors of Cannae.
Winter of 216-215: Hiero dies and is succeeded by his grandson, who opens negotiations with Carthage. He's killed 13 months later, and Syracuse remains loyal to Rome.
214: The leaders of the pro-Carthaginian faction, Hippocrates and Epicydes, are assigned to Leontini. They take control of the garrison, including a large number of Roman deserters, declare independence from Syracuse, and begin raiding the Romans. Marcellus storms Leontini, but H&E escape, win over the Syracusan army sent to support Marcellus, and take control of Syracuse.
213: Marcellus begins the Siege of Syracuse. The initial assault predictably fails, and he takes 1/3 of the Roman force to reclaim rebel cities. Carthage sends 28,000 troops to Agrigentum, and a Syracusan army manages to break through the siege intending to join the Carthaginians but is discovered by Marcellus and destroyed. Marcellus then retreats back to Syracuse with the Carthaginians in pursuit. The Carthaginians break off and head to the interior to gather more allies against Rome.
212: The Romans capture the outer city during a Greek religious festival, and plague hits the Carthaginian army in Sicily. A Carthaginian supply fleet is turned away, and the city finally falls to the Romans.
211: Carthaginian reinforcements arrive and a new commander takes control of continued Carthaginian resistance from Agrigentum. Numidian cavalry raid
Roman lands almost with impunity, but suffer one defeat at the River Himera in the absence of their commander, Muttines. The Carthaginian commander replaces Muttines with his own son.
210: Romans attack Agrigentum. The Numidians, still loyal to Muttines, open the gates for them and Agrigentum is captured. With the Carthaginians removed, most rebel cities quickly return to supporting Rome.

I see two possible PODs.
First, the Romans simply fail to successfully assault the city in 212 B.C.; they don't see the chance, or the Syracusans are on better guard, or... whatever. So, what happens then? Do we have to wait until 210 to break the siege, when Marcellus would likely be recalled to Rome in order to deal with Hannibal's advances, or could the Carthaginian army with support from Sicilian allies successfully break the siege after recieiving reinforcements in 211?
Second, moving further back, Marcellus happens not to run into the Syracusan army marching to Agrigentum in 213. In that case, the full combined force of Carthaginians and Syracusans is available to challenge the Romans, and Marcellus and his third of the Roman army in Sicily is away from the city. Could the combined Carthaginian and Syracusan army either break the siege while Marcellus is away, or attempt to destroy Marcellus's smaller force in isolation before marching on the city?