What if Constantinople had never fallen to the Turks?

[Ironside]

I think (and if you know more, please correct me) that the 1st crusade was due, in part, to byzantium requesting help from the turks. there were several other causes, but byzantium i think called to the pope for help.

They did request help in the form of money and mercs though, not a bunch of unwashed barbarians (byzantine opinion).
Anyway, the first crusade did recapture territories that were given to he Byzantine emperor, who then quarreled with the feudal lords that didn't surrrender those lands as promised.
The first crusade was very beneficial for the Byzantines while the following ones less so.

But generally the internal strength were gone, so any bad emperor had profound negative effects at this point (like weakening the empire enough for the 1204 sacking to be possible).