Sorry she is having trouble.
Egg binding is usually deadly within 48 hours and poo butt is not one of the symptoms that I am aware of... in fact they often can't pass poo but maybe only liquid. Usually no appetite and staying inside the lay box... sometimes tail pumping if they are just standing there. Have you inserted a finger to see if you could feel an egg? How long has she been this way?
Sometimes poo bum is simply a hen that doesn't squat far enough or it could even be a sign of lice or mites in the area (I think). But her skin doesn't look really angry and I can't make out any eggs attached to feather shafts.
Her vent does not look infected or prolapsed to me... but did it look different to you before? In the first pic, I feel like her legs look weird but maybe it's just the blurring. Can you get a clear pic of the legs?
She might be warming up... ill birds have a harder time regulating their body temperature (which is much higher than ours).... I would consider starting a new thread for her! If you still have your video you sent to the farmer of the first gal... You can use vimeo or youtube to upload here if you want us to review.
Sorry I'm can't be more help.
