Determining what causes chicks to die in egg is a complicated process. One thing that is generally best is to lay them on their sides if you don't have an automatic turner and manually rotate them a few times a day. Usually incubating them in cartons just causes problems such as malpositions.
If there were problems in shipping (You would never really know) then that can also cause minor disturbances which add up over time. Also of note, bad genetics can lead to that. I would lean towards bad positioning through incubation and possibly frequent openings as potential causes. I can only speculate because I didn't peek over your shoulder.
Some more generalized causes:
- Incorrect incubation temperature, humidity, turning of eggs (during earlier stage of incubation), ventilation.
- Contamination. (Mother may have been sick or had a minor infection prior to laying)
- Eggs chilled too severely. (Caused by leaving the eggs out of the incubator or if a cold snap happened during shipping)
- Nutritional deficiencies in mother hen (This would happen before you ever got the eggs)
- Embryonic malposition. (Potentially caused by having them in a carton and not turning them. Again, I can't say for certain)
Again, I regret to say I can't give you a surefire answer because I don't have a way of knowing exactly and precisely what you did during the whole incubation period. I'd say go ahead and let the viable egg sit in the incubator and just wait it out. You may have had it too chilly and thus it just needs a few extra days. You can do quick candling by simply holding the flashlight to the large end of the viable egg and not needing to remove it. Keep it short. If your incubator is a still air one, I'm under the impression you should have heat at 102 degrees F. Again, I cannot readily say as I don't know the specifics of your incubator. Mines still air so I do 102. And even then I'm sure I could have gone with lower temps overall.
I have read that it is common for an egg to take 27 to 31 days to hatch. So just give that viable egg some time. Make note of exactly what you did and you can improve. It's not an exact science and frankly I always consider it bordering on voodoo than anything else.
I forget if I linked it but here's the specifics on the float test for egg viability.
https://avianaquamiser.com/posts/float_test_of_egg_viability/
Additional resource to give you some good baselines:
https://www.backyardchickens.com/threads/incubation-and-hatching-guide.595007/
When I first began hatching this thread actually saved the life of my first call duck brood.