How long has she been like this? Was it a gradual onset, of did it happen suddenly? Because of her thinness, I think that she's probably had something wrong for a while. Chickens are, unfortunately, quite adept at disguising illnesses.
Emaciation and lethargy are two symptoms of a high worm infestation. I'd get a dewormer like Safeguard (for goats) or Valbazen. Both dewormers are broad-spectrum, and should get rid of most of the worms. Worming isn't usually recommended on sick birds, but if it is the problem, there's no other choice.
How old is she, and has she been laying? Feel her abdomen. Is it hard or squishy? A hard abdomen might mean that she is egg bound, though if she hasn't been laying, its unlikely. If she's been laying, and is over a year old or so, I might suspect Leukosis. Leukosis causes lethargy, green droppings, and eventual death.
The green droppings are just as likely being caused by her not eating enough. You need to get her to eat. Try offering her some scrambled eggs, or if she won't eat that, try to get her to drink/eat some raw egg. Moistened chicken feed can also entice chickens into eating, as can yogurt and applesauce. Make sure that she drinks enough, too. If you have some, give electrolytes and probiotics, as well as vitamins. If you still can't get her to eat, you should probably look at some information on tube feeding.
Check her for mites and lice. They can sap the energy of a bird, causing weakness. If you see some, dust with Sevin, or spray with a mite spray like Poultry Protector.
