If you're just talking about maintaining the same borders between the Ottomans and the Byzantines as in 1453, I wouldn't say that much changed at all. By that point, Constantinople had ceased to be a major trading hub and the Venetians and Genoese were happily trading with the Ottomans through Galata and other ports. In addition, the Byzantines were essentially vassals of the Ottomans by that point anyway. The lands that were still Byzantine in 1453 never really contributed a huge amount to the Ottoman war effort even after 1453; most of their power came from the bulk of the Balkans that had already been conquered, Anatolia, and the various Ottoman vassal states in the Balkans, Crimea, and North Africa. Constantinople was little more than a trophy for the Ottomans.
In order for a sustained Byzantine Empire to have had much impact on history, I would say we'd have to freeze the borders either pre-Manzikert or post-First Crusade. By the time of the Fourth Crusade, it was already too far decayed to be saved.
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