A lot of people have been posting about sick/lethargic chicks. Unfortunate that it's such a common problem.
I had a salmon faverolle chick that acted much the same after arriving from a long journey through the postal service
Hydration is the key, I think. I felt that administering drops of water (with added vitamins and electrolytes) was more important than feed (at least in the short term) so I didn't force mash or yolks on her (I offered, but she balked)--plus, it only served to stress her out more.
Also, I found a product called Poultry Nutri-Drench at my feed store. It's vitamins in a molasses base and it raises the chick's blood sugar and gives them a quickly-absorbed boost of vitamins and energy.
The chick really seemed to snap back after a day or two of that stuff. I mixed it in the water, and it can also be administered directly with the dropper. I wish I'd had it on the first day of their arrival.
The Faverolle still seems to favor the warmer part of the brooder, and she's developmentally behind the other chicks (maybe because she's kept herself warmer?), but she's now more in sync with them--eating when they eat, snoozing when they snooze...
I can actually stop worrying about her, I think, which is a relief.
Today I noticed her wing feathers have finally shown some real growth, too!
I'm not a saleperson for the Nutri-Drench company or anything
I just had a good experience with the stuff, and plan to keep it on hand for anytime my girls might need a boost, or any future chick orders I may have.
Not saying it would help every chick (who knows what really causes some of these issues?) but it can't hurt, either.