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I understand your logistical constraints. Unfortunately, diarrhea, dehydration (as evidenced by her floppy comb) and thin shelled eggs 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.
It's best to approach the diagnostic process with a clear sense of a bird's 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.
Because 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 or the injectable solution can be given orally for 5-7 days is available in your local feed store as are the other drugs. Consider bringing your sick birds 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.