Give the chick coconut oil. By chilling the oil and making it solid, you can take tiny bits of the oil and slip the pieces into the tiny beak. Try to get at least a fourth teaspoon into the chick. If a poop isn't produced in an hour, repeat the oil. Lube the vent with the oil to soothe the crack...
It does appear the chick has a birth deformity. When you see such a deformity, there are very likely more of the same inside the body. My guess is the chick lacks adequate intestines to handle digestion and elimination of waste.
My method of judging when to euthanize is after there has been...