Because there was no longer any Empire to speak of. Constantinople was the end of the line.

This was the Byzantine 'Empire' in 1453 - a mere city-state that had already been physically surrounded by the Ottoman state since 1387 and blockaded by sea thanks to the construction of Ottoman fortresses along the Bosphorus in 1394.

Some of the European powers may have been inclined to send aid, but it had no way of reaching the city - the Turks were bombarding (and beheading the crews) of ships attempting to run their blockade, and their enormous army, around 200,000 strong, which no European power was capable of taking on, blocked the landward approaches.

Small groups of defenders paid for by private individuals did manage to get into the city, but any large-scale relief effort would have in all likelihood met the same fate as the Hungarian-French relief army of 1396 (crushed with few survivors, its leaders captured).

Bear in mind though relations had improved since the end of the Latin Empire, there was still a great deal of hostility and tension between the Catholic and Orthodox religions - better the Turkish turban than the Papal tiara, as Loukas Notaras, Grand Duke (an office roughly equivalent to Prime Minister) of the Empire observed.

Forget any sense of Christian fraternity - though this did inspire a few small private ventures - to all intents and purposes support from the West was conditional on the Greeks abandoning their faith and accepting Catholicism, as various Popes had made clear. It was too much to swallow for a devout people and a city still reeling from its sack, occupation and desecration by Catholic forces.

As /u/telkanuru pointed out, they were rioting about the prospect of accepting Roman primacy in 1445 when Ottoman troops in their fortresses would have literally been within plain view of any citizen of Constantinople.

After the Fourth Crusade in 1204, Constantinople and much of its surroundings were ruled by a Latin Emperor for some 60 years before the Byzantines re-took the city. The Fourth Crusade, however, had stripped the city of almost all of its wealth, and after the collapse of the crusader states in the Levant the rule of the Byzantine Empire was more or less only confined to the city itself. It was still a major trading center and it possessed imposing fortifications, but the great expanse of empire was no longer there, particularly its tax base in Turkey (see here).

As for your second question: because of the various misdeeds of the Crusades, when the Byzantine Emperors saw the writing on the walls and agreed to accept Roman primacy and practice in exchange for Western aid in an agreement with Pope Eugene IV in 1445, the city of Constantinople rose up in riot. Nonetheless, Eugene's successor, Nicholas V, was appalled to hear of the city's fall eight years later and attempted to raise a crusade among the Italian city states, which remained too involved in their own squabbles to bother.

The Venetian a Genoese troops at Constantinople were there to protect those city states' trading interests, not the city.