Hi,
I'm sorry to hear about your chick. Unfortunately, I too have plenty of experience with this lately. I have been nursing several sick chicks and here are the best methods I've found:
1. Mix some chick starter feed (crumbles) with water or plain yogurt to form a sort of wet mash. You can try either spreading some out on your fingers (if she will peck), or form some into a wet glob and put it in her mouth gently. Sometimes if you 'peck' at her with the food, it will trigger her pecking instinct. Once she gets the hang of it, you can switch to putting the food on a spoon instead of your fingers, and holding that in front of her (much less messy!).
2. Try using just plain yogurt, or just crushed boiled egg yolk every once in a while.
3. My water concoction: Add a couple of drops of baby vitamins to a couple of pints of water. (Brand name is Poly-vi-sol, available in any pharmacy). I use the one without iron, but only because I didn't know if iron would be okay. Also add a small amount of sugar (half a tsp. per two pints) and terramycin (1 tsp. per gallon of the powder that I use).
4. To give her water, we have a small plastic syringe. Suck up some of the water concoction (without using a needle in the syringe!!) and holding the syringe upside down, squirt a little bit of water out of the syringe so that it collects in the small well at the tip of the syringe. Dip the tip of the underside of her beak into this little well of water and capillary action will pull some of the water up into her beak. If she will drink out of a spoon or bowl you won't need to use this method. I find the syringe method to be great because you can control exactly where the water is and it also doesn't make a mess.
5. I feed our babies once every hour or two at first. After the first couple of days, I moved it to every two or three hours.
6. Slowly phase out the yogurt and water and see if she'll start pecking at dry food easily. You can crush the chick starter up into a more powdery consistency, since she can't scratch at it to break it up herself.
7. Once she is strong enough to peck at food on her own, you can put her in a small box with a small dish of food (I use a small plastic container lid). I also keep a tiny teaspoon full of water in there with her and refill it with the water concoction as needed (generally every four or five hours). By keeping it in a teaspoon, there's not a big, wet mess if she spills it.
I have other suggestions if she is unable to move around on her own, just ask! Sorry for the long post.