She is eating, is she drinking? I had one that did not learn to drink when I dipped its beak and did not learn from watching the others. It was acting the way you describe. When I dipped its beak again it stood there and filled up on water. I think that was the chick that grew up to be a not really smart hen, but she grew up and laid eggs.
I think Rosemary is on the right track. It doesn't have to be Nutri-Drench. You may be able to get other electrolytes at the feed store. Some people just mix up some sugar water. I use hummingbird liquid. The idea is to get something in her to give her energy. Put a drop of liquid on the end of her beak with a syringe or medicine dropper, she should swallow it. Keep doing that as long as she swallows it. Don't try to put it down her throat you might drown her.
You said she is moving and eating. How lethargic is she, how much movement? Is she fluffed up or are the feathers normal like the others?
One week old is often the time for a "failure to thrive" to show up. They have used up the nutrients from the yolk they absorbed at hatch and something like a birth defect prevents them from making it any further. Don't be surprised if that chick doesn't make it, but that doesn't mean you don't try.
Good luck and let us know how it goes.
