I find it unlikely that the Fourth Crusade doomed the Byzantines, really. It's always popular to condemn the Fourth Crusade, but it's not really the great betrayal and disaster it's treated as being. It was definitely quite the mess, but while the sack of Constantinople is often pointed to as its greatest failure, it is in many ways the logical conclusion to the events that lead them to that point.

The short version of the Fourth Crusade is that in 1201 secular nobles intending to go on Pope Innocent III's recently called Crusade made a deal with Venice where they commissioned an absurdly large fleet to take the entire army to the Holy Land where they would probably launch an invasion of Egypt. This was the biggest mistake of the whole campaign. Sea voyages were expensive and the Crusade took on a lot of debt to pay for Venice's fleet. They also didn't bother to tell Innocent about the deal until after they had agreed to it, leaving him little choice but to approve it or bring the entire Crusade to an end. It is also important to note that no Crusade had ever left in its entirety from the same point, and this plan required every Crusader from across Europe to come to Venice before leaving for the Holy Land. The Third Crusade is the nearest precedent to this kind of idea, Philip II and Richard I had both sailed their entire armies to Acre, but that Crusade was paid for by kings who had deep coffers. No kings went on the Fourth Crusade.

As you might have guessed, the Crusaders couldn't pay for the fleet when it was completed in 1202 and found themselves in a difficult situation. The Doge of Venice made a deal with them where not only would their debt be forgiven, but also the Venetians would join the Crusade if they just agreed to deal with some enemies of Venice on their way to the Holy Land. The Crusader's sacked the Christian city of Zara, got excommunicated by Innocent, begged forgiveness, and for some reason were given it.

Here's where things get a bit messy. The Crusaders then turned to Constantinople, with the motivation behind this move being still debated by historians. The stated reason for their initial siege of Constantinople was to put Alexius Angelus (son of the recently deposed Emperor Isaac II Angelus, who was still alive but blind and in prison) on the Imperial throne, whereupon a grateful Alexius would pay off the Crusader's debt. Thomas Asbridge doesn't really believe this version, and sees the invisible hand of Venice manipulating this event (they wanted a more pliable Emperor on the throne, or so he assumes). I'm inclined to believe that the Crusaders were primarily interested in getting out of debt and on with their holy war and saw Alexius as a win-win of doing a good dead (restoring a rightful ruler) and getting out of debt for it. In the end Alexius couldn't actually afford to pay the debt, the Crusaders fell out with him, and when he was brutally murdered by a rival family the Crusaders saw it as an opportunity to intervene and do away with an evil tyrant so they invaded and sacked Constantinople, and eventually put an Emperor of their own in control.

So, the whole thing is a mess, basically. However, it's not just a western European mess. In fact, from a purely land-gain perspective the Fourth Crusade is the second most successful Crusade ever. Only the First Crusade added more land to the Crusader States.

What we can see in the Fourth Crusade is a mix of Latin politics, Byzantine politics, and Venetian politics (which is often a mix of the two during this period). Venice was traditionally the only city in High Medieval Italy to still swear loyalty to the Byzantines, but increasingly as time went on this was either mere lip-service, or only used when it was beneficial to the Venetians. A combination of Venetian greed, Byzantine instability (it's worth mentioning that Isaac II had become emperor by deposing Andronikos Komnenos in 1185), and good old fashioned Crusader zeal (and no doubt a decent helping of greed) is really what made this whole campaign a mess. It should also be noted that some Crusaders didn't join in this detour, and instead sailed directly to the Holy Land on ships they paid for themselves (mostly from Marseilles).