That is terrible about your hens problem. First, I would remove the hen. The cock is trying to get her to get up and handle the babies, which she can't in her state. Have you checked her lower vent area?
I am trying to put the pieces together Jang. It concerns me that she is not actively standing up and can not fly, though she tries.
I am also thinking she may be eggbound as Mary suggested earlier.The area where a pigeon expells their waste and the egg for females, is the vent area. Look and see if it is gummed up or obstructed in any way.
Do they eat well?
Is the water clean?
Does she have all her feathers...check the throat for canker?
Are you suppling her and the rest of you pigeons with grit? A female that has produced eggs especially needs grit with calcium. It is the grey color.
I have to get some sleep, but I see you are still up. Here is a link that I want you to read that was written by one of our well respected pigeon rescuers named Pidgey.I will check on your post later in the day.