One of the chicks that hatched yesterday dried out hard like it is coated in glue. It can only move its legs and beak. Its not doing well at all. I tried cleaning it with warm water and that softened it up but only until it dried again. Should I try dish soap?
No; do not use dish soap. What I believe you're running into, the sticky substance, is likely the albumin, maybe the chorion, but more likely the albumin. The chorion envelops the chick and all membranes providing an overall enclosure during development; the albumin is what is left outside this envelope, and it's the white of the egg, the sticky part. Like getting dried egg whites off a plate, getting them off a chick takes the same thing: water, but only water. You just have to apply it differently.
Instead of washing under water, try using a bowl of hot water (yes, hot because it will cool quickly) and a SOFT "wet" washcloth to wipe the chick off. Keep a 2nd "drying" (dry) soft washcloth on hand and several Q-tips. Try to do this under a warm light bulb to keep the chick warm. For the water temp, use a thermometer and make your water right at 100 degrees. This will not hurt the chick; they just hatched from nearly 100 degrees in the incubator and require about 95 degrees when dried and in the brooder.
Back to cleaning: You'll need to do this very gently as you don't want to irritate the chick's delicate skin and downy feathers, but you want to get this off as it can bind the skin too as you've found! This is also the reason for very SOFT washcloths.
First, dip a Q-tip into the water and quickly check that it's nice and warm, then rub it gently over the seem between the eyelids then around the whole eye area following the trend of the feathers - wipe in the direction the feathers go or from the front to the back of the bird. Go over it a few times right where the lids meet with just enough warm/hot water on the Q-tip to leave noticeable water on the lids and surrounding eye area. Go over it again and pat it dry with another washcloth. Do the other eye with another Q-tip, and check your water temperature to make sure it isn't going cold. If you still sense moist/wet membrane on the skin (you'll sortof be able to see it once wet), go over the area a third or fourth time using new Q-tips each time - the old ones are collecting the sticky membrane. Once wet, you can VERY CAREFULLY go in the opposite direction of the feathers, but be careful to be extra delicate so as not to remove the feathers around the eye. Gently pat dry between each attempt with a Q-tip with the "drying" (dry) washcloth. Do the other eye the same as the first.
Now, you're going to do the rest of the body with the "wet" washcloth instead of the Q-tip, but check that your water is still hot, about 98-100 degrees. Dip a small section of the "wet" washcloth in the warm/hot water, wring it out slightly by gently pinching it, and wipe the chick down starting at the beak/head and working around the body to the tail. The washcloth needs to be wet, but not dripping, wet but not just moist. Do a section at a time using a new section of the washcloth for each section. You may need to wipe each section a couple to three times to moisten and remove the membranous material of the albumin. Pat to damp with the "drying" (dry) washcloth after two to four good wipes with the wet cloth. Do this all over the chick's body, making sure that your water stays warm/hot, doing a section at a time.
Once you're done, put the chick in a warm spot to dry (incubator is good for this since they're slightly wet after doing this), or put them in a brooder with good steady heat to dry. You'll likely find that you didn't get all the sticky off, but you did get a lot of it. So, you may need to have a few more of these chicken washing sessions to remove all the sticky from the chick. Try again tomorrow when the chick has dried and recouped a little from the trauma of its first bathing. We've done it, and when you finally get all that sticky off, the chick will be as fluffy and happy as the rest of her hatch-mates...