We had a similar problem with our chicks when we first got them. We bought 8 chicks - three month-olds and five week-olds. After a couple of days, we noticed that one of the month-olds was behaving just as you described. No energy, just seemed to stand in place sleeping all the time. Wasn't eating. Drank only when we held it and put the beak into the water. I was sure we were going to lose it as day after day went by with no food and the bird got lighter and lighter all the time. Meanwhile, on day 6 after we got them, one of the week-olds developed the same symptoms. I'm sad to say, the week-old lived only a few hours. The month-old on the other hand, ate for the first time voluntarily right after the younger one passed. I still wasn't optimistic it would survive as it was so weak by that time I was sure it was too little, too late. For the first couple of days, it would eat only 2-3 bites at a time before being too exhausted to continue. But as its strength returned, it started being able to eat more and more. It took weeks for full recovery (measured by catching up in weight to the other two month-olds) but that chick is now a rooster of 18 weeks old, head of the flock and just learning to crow.
I wish I had some advice for you but in truth, I have no idea what this "illness" is or what you can do to cure it that you aren't already doing. I can only suggest keeping it warm so that its weak body doesn't have to expend too much energy on that. Continue to offer liquids to ensure it stays hydrated. For water, take a 2-cup measuring cup, add a tablespoon of honey and a tablespoon of ACV and feed the chick from this water. This will hydrate while also giving a slight boost in energy and a little boost to the immune system. I didn't have much success getting my chick to eat, but did try the following: semi-soft boiled egg yolk, yogurt, oatmeal, or make a mash out of the chick starter by adding enough warm water to make it into a mash-like consistency. If you can get yours to take a mouthful of two of sustenance every few hours, and keep it hydrated and warm, that may be the best you can do and let mother nature do the rest. Good luck!