What if Constantinople had never fallen to the Turks?

[Subotan]

This is as silly as question as asking "What would have happened if Berlin had not fallen to the Russians in 1945?". However, the theme is quite interesting, and the roots go back much further than 1453.
Had Manziker, Myriocephalum and 1204 not happened, then maybe we would have had a longer lasting Byzantine Empire.

let me clear up what i think Vladimir is saying:

the Byzantines, like the original Romans before them, screwed themselves with all the murderous politics, constant rebellions, over-reaching their boundaries, etc. So in a way, you could say that they caused their own downfall with internal turmoil, and the Turks were simply that little extra tip in the wrong direction needed to destroy it.

Not nessecarily. It weakened their ability to resist, but it wasn't the cause. Politics had been happening for centuries before the Turks, and the Avars, Pechengs, Magyars, Bulgars, Arabs, Rus etc. had all failed to defeat "Romania".

I agree, in a sense. the 4th Crusade was indeed like punching a geriatric in the head, the death wasn't immediate, but it pretty much sealed Byzantium's fate two and half centuries down the road.
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This.

One of the most important developments, had Byzantium somehow survivied a few more years, is that the Battle of the Mohacs would probably not have happened, leading to an independent Hungary/Bohemia in Europe....