Most day old leg issues are vitamin problems in the parents or injuries. Need pictures to determine what is wrong exactly. Link has a picture of most of them and is very informative. If none it may be something else. Treatment for this is typically splint leg into correct position and give missing nutrient (vitamin supplement).http://http://www.apa-abayouthpoultryclub.org/Edu_Material/VITAMINS.pdf
These are just the most common I know of. This chicken won't be a show chicken but the sooner treated the better the chances of just being a laying hen/productive rooster/dinner. I don't have enough info for anything too accurate to determine whats wrong but this may be a start.
(list for picture below)
1. vitamin a
2. vitamin e
3. vitamin k
4. crazy chicken disease
5. Pantothentic Acid
6. Riboflavin (I think)
7. Vitamin B
8. Vitamin D
New here, I don't know what happened to my last response. However, thank you for the nice replies. The chick died that same day. The leg seemed stiff like it couldn't extend it, similar to #6 I guess but both legs.
Anyway thanks for the info.
I don't think it was Riboflavin (vitamin G #6) because the toes aren't curled. Vitamin D (#8) is unlikely because that chick is likely 4 weeks old in a dark tunnel industrial poultry house. It's the sunshine deficiency.
I think since it's a day old it has to be some sort of a birth defect. It must of been severe. There isn't much you can do for those except broad multi vitamin and splinting. If you give me some time I will try to come back with a better answer.
Edited for better answer. Because your chick was a day old,
A mild vitamin A deficiency (#1 to the right) which would cause skeletal and organ problems. Death occurs quickly with this one and if severe the egg won't hatch at all.
Incubation Error in Temperature, Turning, or Humidity (this causes problems with development)
In all cases, there would of been little you could of done. I am sorry for your loss
Thank you for your exceptionally thoughtful response. I really appreciate it. This was our first time incubating and I took massive amounts of notes but have yet to really analyze. I think we did several things wrong as only 7 hatched out of 18 and one died. I do feel guilty but appreciate you saying there wasn't much I could have done. I'm scared to try the incubation again even though I was fascinated by the whole process.
Don't be scared, for your first time this is normal. This is where the saying comes from of "don't count your chickens before they hatch" comes from.
With more experience the survival rates go up the mistakes go down and really it isn't a bad thing. It's never expected you hatch all of them, even in the commercial poultry. In commercial poultry, they just identify the ones that won't hatch more quickly and get rid of them and everything is super computerized and even still will have some that won't hatch.
You probably incubated some duds where they weren't fertile at all. A lot of people are having trouble with their hatches too because of the weather is throwing off the shipments. When they get thrown off, it can contribute to a lot of birth defects and not hatching eggs.
So, don't get discouraged. What my family does to incubate eggs is use a hova-bator with auto turning. About 75-95% hatch if the duds were candled and removed early. My little cousin did a science fair project on hatching eggs and found both manual and auto turning to hatched equally so it's not the method you use that contributes at all. They used buff orpingtons for the experiment. But, even my cousin isn't always successful.
Expect a little loss with chicks but it can be a rewarding experience. The reason is nature just isn't perfect.
If the chick that died had a vitamin A deficiency, he may of been mild. The others may of been severe and that's why they didn't hatch. In a severe case, The circulatory system and kidneys wouldn't develop at all. Death occurs in severe cases at 48 hours of incubation because nothing developed at all to continue. This can occur when the adult chickens don't have it in their food and water and they can't forage for it. It's in leafy green plants. The apa poultry vitamin deficiency has more on what foods contain it. It can be a winter chicken problem but it doesn't affect them as bad as it does chicks.
It could of been a rough shipment and a lot of shipment companies got hit hard by the storms. It's the leading cause of error in incubation especially in hatching chicks in the past week. Trust me, I helped a couple people today with something a long the lines of chick has issue and shipment had issue. You can't control the weather. Incubation error is not often the error of the hatching person but just a broad term describing a problem happened with incubation.
If it was disease, (which is a possibility but I really doubt it because he was born that way and disease takes longer than seconds but threw it in there to cover my bases) there isn't much you can do for a day old chick. They are just too weak to handle most interventions you could use on an adult.
So the moral of the story of this post is, you are not alone and everyone is having issues with their hatch. You can't control everything that goes wrong with the hatch. The remaining eggs could of just been infertile eggs or just not meant to be. I wouldn't get disheartened because a lot of people have had bad hatches this week and this is just your very first one. I don't recommend cracking them and doing an autopsy of sorts. It will smell bad.
My strongest bet is shipment error because it is the most common one today or vitamin A deficiency in hens. I'm sorry for the wall of text. I am also sorry for your loss. I know it isn't fun but this was truly out of your hands. Hatching can be a lot of luck sometimes.