Is abdominal pain with fever generally an emergency only if the abdominal pain is severe or if the fever is 104 or greater?

No exclusions!: Not all bad things that occur in the abdomen are associated with high fever (example: acute intestinal ischemia) nor does the pain have to be severe (example: cancer is often painless). Remember, the abdomen includes many organ systems (gi tract, liver/biliary/pancreas, renal/urologic, gynecologic, vascular, etc.)--any one of which can cause catastrophic illness without severe discomfort or fever.