Doesn't sound like egg-bound, but definitely not well. Separate her from the others, get her some apple cider vinegar and/or yogurt, electrolytes, and antibiotics if you can. Keep that vent clean and clear of obstructions. Feed her some olive oil or fish oil if she doesn't poop for 1-2 hours...
Is she the only one with black spots on her comb? If they're not preventing her from eating & drinking, & they haven't drawn blood, it should be fine. Sounds like you have plenty of room for that number of chickens. Is she a recent addition?
Try yogurt, flavored or plain. Chickens usually love it, and it may help with any intestinal stuff she's got going on. If she won't eat that try apple cider vinegar -- not many calories, but it may help her beat whatever she's fighting.