You have changed History!  Hannibal knew it was inevitable that he would have to invade Rome by land.  Gambling that he could both destroy the Roman army, and take their navy would have been foolish.  Then, not being able to invade Italy with that navy would have made the entire undertaking worthless.  Most likely, the Romans, if in danger of defeat, would simply have withdrawn to their ships and sailed away.  Hannibal had very little chance to gain the decisive victory he needed.  Scroll down to see what he actually did.

    Though he had to do some fast talking to inspire his men, Hannibal convinced them that the best course was to stay on track and cross the Alps.  Still, it was no easy journey.  Many mountain men lived in the Alps, and they resisted Hannibal's advance by throwing rocks down upon his men from ledges above.  Often the snow and ice gave way underfoot, and men plummeted to their deaths.  Most difficult of his equipment to move were the elephants, and Hannibal lost most of these to the narrow paths, or the cold.  Only the sight of the lush valleys below, and the thought of verdant lands they would own kept his men moving forward.  Soon, he would have another choice to make.

    Hannibal inspired his men by reminding them that they were now all veteran soldiers, whereas their opponents would be largely composed of new recruits.  This brings in what I call the Leadership Factor.  Every time the Roman consulship changed, so did the leadership of the Roman army.  Napoleon is supposed to have said that it is "better to have one bad General than two good ones", which may have been intended to refer to Rome.  The Carthaginians had only one man to follow, so as long as he could inspire them.  Hannibal's charisma often caused his army to achieve feats seemingly beyond their capacity.  Here, he emphasized their team spirit, the great treasure in Rome, and the indisputable truth that recrossing the Alps would be impossible.  He brought in prisoners, and had them fight each other to the death, promising the winner a free pass home.  This roused his soldiers into a fighting frenzy.
    This is also a good time to mention the Specificity of Orders Problem, which will also soon come into play.  (It is a good idea to remember these various Factors and Problems, since they may help you make decisions later.)  Roman consuls are given orders by the Senate, which inhibit the actions they can take.  As a matter of self-protection, the Senate never allowed the two consuls to have their armies in the same area at the same time.  This prevented the two consuls from fighting (at a cost of Roman lives) with each other, and also prevented them from conspiring to lead the army into Rome and take over.
    At this point, the consul in charge of the Roman army that had been sent north was named Scipio.  (The other consul, Sempronius, was sent south, to work his way to Sicily, and thence onto Africa, where he might attack Carthage itself.)  He was building a bridge across the Ticinus branch of the Po river, when word came from scouts that Hannibal and his men were only 5 miles away.  Hannibal was fully aware of Scipio's presence, but debated his best course of action.  He could attack now, wading across the river to meet the Romans, or he could wait, letting them finish their bridge and come to his side.  His men were still somewhat tired from their trip over the Alps, and in hostile territory.  Quick action, though, might prevent the Romans from bringing the full might of their army upon him.  Which would you choose to do?
Attack the Romans now.
Wait until the bridge is built.