I am sorry to hear about your hen. It is so hard when they get sick. Have you looked online for the symptoms of parathyphoid and how it is transmitted? Does that sound like something your hen could've contracted? What I have read says that the mortality rate is very low. That being said, she is sick, the question is, with what?
Try bringing her in the house or garage where it is warm. Give her a safe and cozy place of her own. Then try and give her anything that a chicken might like. Pieces of fruit, scrambled eggs, cooked oatmeal, yogurt, etc. Get her some vitamins, poly-vi-sol with no iron. There are a lot of post on BYC that talk about how to feed and care for the sick ones. Check and see if she is drinking. No water will kill her faster than no food. Try dribbling some on the sides of her beak and see if she will drink it. Don't squirt it down her throat, you could drown her easily.
Also, could she be egg bound? I have never had one do that, but again check on the forum for that. There is a bunch of information on how to check for it, and how to treat it. Also, feel her crop and see if it is empty. If she is not eating, it should be. If it is hard, then it may be impacted and again, search the boards for info.
The best you can give her is supportive care. If she is breathing ok and her eyes are clear then it probably isn't an infection.
I hope things work out for you.