Can a doctor turn away a patient if they didn't have any money?

Not if they are working in a hospital. A private practitioner may turn someone away, but never someone in a hospital.

Also, a private practitioner may not turn someone away due to inability to pay if the person is in a life-threatening situation or a medical emergency, such as a person in respiratory arrest (not breathing), experiencing a seizure, or who just suffered a stroke. They must either assist/treat the patient until they are considered "stable" (at which point they could then go obtain help elsewhere) or get them help from someone else, but if no one else is there and they must wait, in the meantime they must do whatever necessary to try to keep them alive or get them relatively stable.