I'm sorry to hear of this with your hen. She has symptoms referable to her respiratory tract (infraorbital sinus infection associated with that red eye?), her gastrointestinal tract (runny poop), is anorexic and has stopped laying (nonspecific signs of illness). Unfortunately, these symptoms can indicate any number of illnesses or health issues in chickens. In avian medicine, there's rarely one cause of such a presentation, so we usually begin with a list of differential diagnoses and use lab tests, X-rays, and physical exams to differentiate one from another. Necropsy of a newly dead or a sacrificed severely ill bird then refrigerated (not frozen) can be an important diagnostic particularly in large flocks. With this in mind, your best course of action is to reach out to your county-extension poultry personnel or avian-oriented veterinarian (please see here: www.aav.org) for help in arranging a necropsy if you have a large flock. An avian vet would still be ideal for such a hen.
It's best to approach the diagnostic process with a clear sense of her financial value to your operation. Although some services such as your county animal disease diagnostic laboratory might be available free of charge through a county agency or land-grant extension office, the expense of some diagnostic tests and treatments can add up quickly. While it’s always worth your time and money to identify a bacterial or viral infection that could potentially impact more than one member of the flock, this might not be the case with a condition that only affects one hen. It frustrates me that I can't be more specific for you but such is the dilemma of poultry owners and vets alike.
If you don't have an avian vet available to you, presumptive treatment for the most common gastrointestinal parasites plus a broad spectrum antibiotic are reasonable. Piperazine (Wazine, e.g.) will address roundworms and amprolium (Corid) will address coccidia. Tylosin (Tylan-50) dosed at 20-30 mg/lb once daily intramuscularly into her breast muscle or the injectable solution can be given orally (it's quite distateful, however) for 5-7 days is available in many feed stores and online as are the other drugs. It's best to bring her inside as shown here: http://www.the-chicken-chick.com/2015/02/how-to-help-sick-chicken.html
Please respond with further questions or concerns if you wish.