I can't be certain what illness she has but it may be a gut disorder. If she hasn't been eating for four days she is at deaths door - four days without food is a very long time. Feel her crop, if there is still anything in it, is it hard/squishy/empty? She could have compact crop which would make it painful for her to eat. Then check her for parasites, mites can cause birds to become weak and lethargic due to blood loss. What colour are her droppings? Does she have white diarrhea? Is there worms/segments of worms in them? Tapeworms can cause a blocked gut when infestations are serious. What is her bedding? Dirt or hay? Parasites are easily picked up if birds live in dirt and dust. I suggest putting soluble vitamins in her water for three days and synbiotic for the three days after that. I use Soluvite but there is many vitamins available. As a last resort, you could use a syringe to feed he soft safe foods like yogurt. Make sure you only give her little bits at a time and put is above the tongue. Also give her water using a syringe. I think think hand feeding her is required at this stage.
I once heard of a condition other breeders called 'Waste Away'. I haven't researched it much but it can be caused by inbreeding and breeding with younger pullets. The bird basically doesn't eat or drink and dies of starvation, but then again, I haven't done much research on this so many details are missing here.
I hope your hen gets better.
Cuckoo Orpington
