It is best if you can contain the state vet in your area to get a necropsy. They do testing and can usually find a cause of death. Price varies by state, and it costs less in states that have a lot of poultry. It is about $25 in CA and OH, and over a hundred dollars in some states. A backyard chicken usually costs less if you tell them.
I do a brief home necropsy on my chickens that die. Most have some form of reproductive issue, such as salpingitis with lash egg material from internal laying, ascites (water belly,) cancer, or fatty liver disease. If you ever do one, use a very sharp knife and scissors to open the belly from the vent to the breast bone. Take pictures of the organs you see, and many will give opinions of what pictures you post. It is never easy, and the first few times it can be pretty nauseating if you have never but hered a chicken. But seeing what might haved caused their death can be very educational.
Don’t beat yourself up - you tried.
