Being broody can drain most of the health and vigor from a hen. They often come away from their broody stint with parasites because they've been confined and can't dust bathe. Their body can emerge from being broody in starvation mode. This can make them weak and sick and susceptible to the cold.
Not having access to adequate grit for so long can slow their digestive system down to a slow crawl. Crop disorders can be the result. She may also have worms that are slowing the crop.
Here's what I suggest:
1. Worm her.
2. Give her warm sugar water and some soft boiled cooked egg still warm. Follow up with a week of high protein extra feedings.
3. Give her some grit that she can nibble at will.
4. If it's colder than 55F, give her some heat to warm herself.
5. Look her over carefully for lice. You would see them running around on the skin near her vent. Treat with poultry dusting powder if you see them. Give her the means to dust bathe.