Unless you took your bird to a veterinarian to have a necropsy performed, there is no way to determine the cause of death.
Birds are flock animals and I have seen my birds, though they are different species act like they were upset about one of the flock dying, however I don't know why the ringneck might be shivering because they can handle temperatures down to freezing.....you don't by chance have mice at your house, do you...that would be something the other birds might be upset about, if they saw a mouse in or around the cage...if the mouse is still around, maybe in the bottom of the cage, that might explain their fear.....
A few years ago, I lost a nanday to a spider bite...her cagemate killed the spider and would attack any spider he saw after that, but he or the rest of my birds did not shiver or quit eating.....