How long before a dead chicken becomes inedible?
I will post as an answer as too long for comment, but would support closing as opinion based with no definitive answer.

When I raise meat chickens, my answer was zero.  Even if the cause was harmless, the meat would be low quality at best due to lack of ability to remove blood.  Even simple heart failure, besides the lack of ability to purge blood, could result in contamination from systemic issues related to poor circulation.  Note that consumption of down birds was blamed for spreading Avian Influenza in Asia.  The use of down animals was responsible for a widespread Mad Cow recall in US and Canada a few years ago.

At times, and in many cultures, using down animals, either dead or dying, has ranged from acceptable to taboo.  I personally side with the taboo argument.  I hate to waste an animal, but the risks are too high for me.