Viral Gastroenteritis: This diagnosis is the most likely due to the combination of gastrointestinal symptoms (abdominal pain, diarrhea) and respiratory symptoms (cough, runny nose), which can be caused by a viral infection affecting both systems.

Influenza: Influenza can cause both respiratory symptoms (cough, runny nose) and gastrointestinal symptoms (abdominal pain, diarrhea), especially in children.
Common Cold with Gastrointestinal Involvement: While the common cold primarily affects the respiratory system, some viruses can also cause gastrointestinal symptoms.
Food Poisoning: Certain types of food poisoning can cause both gastrointestinal and some respiratory symptoms, depending on the pathogen involved.

Pneumonia: Although pneumonia primarily presents with respiratory symptoms, abdominal pain can occur due to referred pain or secondary infection. Missing pneumonia can lead to severe consequences.
Appendicitis: While appendicitis typically presents with abdominal pain, nausea, and vomiting, some cases can have atypical presentations, including initial symptoms that might resemble a gastrointestinal infection.
Intussusception: A condition where a part of the intestine slides into an adjacent part, which can cause abdominal pain, vomiting, and sometimes respiratory symptoms if the child is in significant distress.

Hantavirus: A viral infection that can cause hantavirus pulmonary syndrome (HPS) and hemorrhagic fever with renal syndrome (HFRS), presenting with both respiratory and gastrointestinal symptoms.
Lymphoma: Certain types of lymphoma can cause a wide range of symptoms, including cough, abdominal pain, and diarrhea, due to the involvement of various body systems.
Immunodeficiency Disorders: Conditions like HIV/AIDS or primary immunodeficiency disorders can lead to a variety of infections that might present with the combination of symptoms described.