Diarrhea can be from infection, worms, etc.
Some healthy hens always seem to have poo stuck to their feathers, but if this is new and plus she is acting ill, I'd definitely consider that it could be diarrhea.
With her moving slowly I would do a complete examination of her. Check her crop in the morning to see if it is empty as it should be, check her abdomen to make sure it is not puffy/swollen, check her feet/undersides. Check for mites/lice, and consider worms.
How is her breathing? Does she keep her eyes closed? You can consider checking inside her vent for a stuck egg with gloves and lubricant veg oil or other lubricant.
Check alongside her keel on either side of her chest to see if she is skinny. Compare her to the other hens. You should be able to feel some meat on her bones on either side.
How is her fresh poo when it hits the ground...watery? Formed?