If she has been like this for a month then she must be eating and drinking from time to time, or she would not have survived this long.
Does she have any unususal symptoms - what is her poo like? Is she lethargic, fluffed up, or just sitting there kind of 'zoned out'?
What does she do if you try to pick her up and move her - resist, go back to her original place, just sit back down where you put her? Where is she choosing to sit - in a nest box or secluded, enclosed place, or out in the open somewhere?
What you describe in your first post sounds a lot like broody behaviour, especially if it has been going on for a few weeks. I have only ever had one broody - also a red star - and she was an excellent mum! She was also very very persistent. Once she got broody and I couldn't get any day old chicks for her to raise (I don't have a rooster, so no fertile eggs). She sat on the nest for over a month before I got chicks for her! (Normal brooding time is 21 days).
If you can give us as much information as possible about your chicken and her behaviour then we might be able to come up with some more suggestions.