In my humble opinion, the turning point in Goblet of Fire, or maybe the whole of the Potter series, was when:
- Harry was wandering around in Hogwarts in the middle of night with the Marauder's Map
- Impostor Moody/Barty Crouch Jr searching Snape's office for Polyjuice Potion's ingredients
- Harry wondering why would Barty Crouch Sr be inside Snape's office at that time
- Snape catching Harry in the dark without warning
- Marauder's Map flying away from Harry's hand and landing on the floor
- Moody/Crouch Jr approaching and saving Harry from Snape
- Snape leaves, Moody/Crouch Jr picks up the Map and takes a look at it and leaves him stupefied (pun unintended) for a moment as he realises he was so close to becoming unmasked...
Now, the question is why didn't Harry use the Summoning Charm to get the Map from the floor? He still held his wand if I'm not mistaken; a quick and quiet "Accio" from underneath the Invisibility Cloak should have served the purpose.
Harry had not too earlier proved to be quite an expert at the Summoning Charm itself, when he summoned his Broom (which was locked up far away inside the school, so it should have needed one of the best Summoning Charms for it to break away the chains binding it) when facing the dragon for the first task.
If Harry had really used the Charm for getting the Map, then of course as the impostor Moody approached, Harry would've seen that the Map was still showing Barty Crouch, and he would have realized it was an impostor and alerted Dumbledore. This would have prevented Cedric's murder and ultimately stopped Voldemort's return, at least for the time being, as Voldemort needed Harry to complete his return to his original form. The whole series would have taken another course.
So, why didn't Harry use the Charm, which should have been in the top of his mind coming out fresh from the first task? Did he just miss using it at that particular moment, or would it not have worked from underneath the Cloak?