Parents first time with chickens, didn't know what to do had to put one down.

So my parents got 4 baby chicks yesterday got them all they need by what the store said they have chick crumbles, a tub deffinately big enough, bedding, a heating lamp to heat the tub to 90 degrees, and some vitamin things for there water. I don't know what happened but today they had some bad luck, my 6 year old brother not thinking went downstairs to look at them and left the door open and our young cat got in there tub and attacked them. From what we could tell none of them were hurt, no blood, broken bones, any of that, they just seemed traumatised. Well about 6 hours later when I was in the room with them working on the computer one out of the silence one of the chicks started chirping very very loudly louder than i've ever heard them. I looked into the tub and the one that was chirping loudly was laying on its but with its wings spread out after about 10 seconds of that it started running around the tub in circles with its wings out chirping the whole time and it's head started to loll backwards. Then it fell backwards on its back and kicked its legs out behind it and stopped chirping with its eyes wide open. Then after a few seconds it would chirp loudly again and then stop. I was pretty sure it was dying but now I don't know. I had my parents come in and my dad picked it up and it seemed to calm down a little but, still would randomly chirp loudly and one second look dead and the next would chirp. It wouldn't stop this process and sounded like it was in a huge amount of pain. So my dad had to put it down. I read online afterwards about some sort of thing called wryneck which it sounded like from the neck bending backwards and falling over. But I never saw anything about the chicks sticking they're legs out and on there backs looking dead or screaming bloody murder. If someone knows anything that could have happened or if it was most likely the cat hurt the chicks more badly than it looked let me know. I did notice that after that happened we changed there water and they have been drinking non-stop for about 10 minutes.