Psyberianhusky, in Italy the country is ruled by the parliament, not the party which wins elections. Whoever gets the support of a majority in the parliament can be PM.
After a PM resigns, the president of the republic meets with representatives of all parties currently in parliament. He proposes a course of action ( nominate a new PM, renominate the old PM, or, if all options fail, he "closes" the parliament(what is the right word?) and starts new elections) and then see if it has enough support.
In this case, he decided for a technical government instead of a political one. In a quite good political move, he nominated Monti senator for life, which is an effective way of telling the parliament his choice, before Berlusconi even resigned. This allowed the head of parties to consider support of Monti's government and to convince their own parties. Berlusconi for example, met some resistance in his own party. If Napolitano's decision had been more vague, then it might have been impossible to create a new government before the stock exchange opens on Monday.
Scriver, he may want to run for presidency, but unless he changes the constitution, it is not going to happen. At the moment, the president of the republic is elected by a very large majority in the parliament, one which it would be very hard to reach without support of other parties, and traditionally it is a person agreed by everybody to be impartial.
He would never be elected in such a system.
People said he wanted to change Italy into a presidential republic, so that he could be elected directly. But now he isn't in a position where he can do such changes.