Patients with some 'illnesses', for ex: King Epidemic, won't go anywhere else for further diagnoses after the general practitioner. This is with a Ward/general diag/psychiatry all available. It says they have used all of the diagnosis machines available, but that clearly isn't the case.

Any ideas on what to do about this?

This happens often. Basically the game tells you that with your diagnosis rooms your current GP cannot figure out what is the disease.

Typically, you need to get more diagnosis rooms researched. Once you get scanner, x-ray or other additional diagnosis equipment you will be able to diagnose the patient. You get this additional equipment once it is researched. You can check the progress in one of the "buttons" on the lower left side of the screen.

Also check if your GP has high skills. A consultant often can diagnose things that a usual doctor cannot.

Hi! The game starts with simple diagnosis rooms incapable of providing data helpful to the GP's further diagnosis of the case. It just means you need to advance. Using consultant-level doctors as GP's helps. If you could solve every problem straightaway, that would be boring, and you wouldn't be eager to uncover new diagnosis rooms in later levels, or be dazzled by the shiny new equipment and delightful animations. Imagine using "Cardio" to help a GP diagnose a Psych case e.g. King Syndrome: that should seem nonsensical. If you watch, Bloaty-Head cases will only ever be sent to one of two rooms: GD or Cardio. These provide the data needed to narrow down the exact type of BH. King Syndrome cases only ever go to X-ray or Scanner. They provide whatever is relevant to KS.