If this came on suddenly, and now she is unable to stand, and if I understand correctly, she is trying to support her self with her wings held out pressing on the floor for balance, then it sounds like poisoning of some kind. Something toxic entered the coop and somehow got into your hen.
Either someone stopped by and brought this into the coop, or it was a toxic insect that crawled in and your hen ate it. Have you noticed any darkling beetles in your coop. They usually will hide under things where it's kind of damp.
If this is what's making your hen sick, you might be able to make her better by giving her a molasses flush. If you think you can get her to eat it, you can put a tablespoon of molasses in a cup of very wet feed and mix it up.
If you can't get her to eat, then you might be able to get some water down her with some Epsom salt in it, one teaspoon in a cup of water. This will purge her intestines and make her poop out the poison that still in there. Then vitamin E 400iu with a sliver of selenium might repair the neurological damage.