Lots of things cause neurotoxin poisoning. Bad feed gone moldy can cause these symptoms, including respiratory problems. The slightest exposure to any petroleum distillates - I recently had a four-week old chick pick up some contaminated grit under a log splitter and within minutes, it was showing all the symptoms your chick is experiencing. Toxic plants. Marek's. Insecticides.
For some reason I suspect Marek's. The chick is the right age for developing symptoms after exposure soon after hatch. But not all chicks will die. They can recover, though they will still carry the virus.
Since you got the chicks from a private breeder, Marek's is all the more likely. A virus such as Marek's can be present in a flock where most of the chickens are not symptomatic. Flock managers usually won't think the worst when they're only losing a chicken once every few years, thinking it's normal attrition. With these viruses, many chickens can develop resistance and live normal lives, even though they carry a deadly disease.
My flock is infected with such a virus (lymphotic leucosis). Most of them are perfectly normal and healthy, having built a resistance to the virus. I even have a hen who is nine years old, and all the symptoms she shows is a small tumor over one eye. Yet other chickens have taken sick and I've had to euthanize them. The most recent was a week ago. A six-year old hen had developed tumors that were affecting her organs, obvious from her bluish-purple comb and lethargic behavior.
The thing about these viruses is they're extremely contagious and if you have Marek's in your flock, you will need to be very careful about exporting the disease. You will not be able to rehome any chickens, or sell any chicks. I had a BYCer ask me if I would sell them some hatching eggs. I had to turn them down explaining the virus in my flock is transmitted from hen to fertilized egg. Marek's doesn't vertically infect eggs, but it does hitchhike on shoes, dander, even air currents. There is no cure for these viruses. But if you discover Marek's in your flock, there is a vaccination for new chicks you might get in the future so they can develop resistance.