Diabetic Ketoacidosis (DKA): This condition is characterized by the presence of ketones in the urine, which is a result of the body breaking down fat for energy instead of glucose due to insufficient insulin levels. Vomiting can be a symptom of DKA, and the high level of ketones (80) in the urine supports this diagnosis.

Gastroenteritis with Dehydration: Severe vomiting from gastroenteritis can lead to dehydration, which in turn can cause the body to produce ketones as it starts breaking down fat for energy. Although the ketone level is high, this could still be a consideration, especially if the child has been vomiting for an extended period.
Starvation Ketosis: If the child has not been eating due to vomiting or other reasons, the body may start breaking down fat for energy, leading to ketosis. This could be a possibility if the vomiting has led to significant caloric deprivation.

Inborn Errors of Metabolism: Certain metabolic disorders can lead to ketosis and vomiting. Although less common, these conditions can be life-threatening if not promptly diagnosed and treated. Examples include disorders of fatty acid oxidation and organic acidemias.
Toxic Ingestion: Ingestion of certain toxins, such as salicylates (aspirin), can lead to metabolic acidosis and ketosis. Vomiting could be a symptom of the ingestion.

Ketotic Hypoglycemia: This condition is characterized by low blood glucose levels accompanied by ketosis. It's more common in young children and can be triggered by fasting or inadequate glucose intake, leading to vomiting.
Alcoholic Ketoacidosis: Although rare in children, if there's a history of alcohol ingestion, this could be a consideration. However, it's less likely given the context of the question focusing on a child.