The presentation of multiple missing teeth (hypodontia), conical-shaped teeth, and inability to sweat (anhidrosis) strongly indicates ectodermal dysplasia, a genetic disorder affecting ectodermal structures such as teeth, hair, nails, and sweat glands. The inability to sweat leads to problems with thermoregulation, which is a hallmark of this condition. The characteristic dental abnormalities, especially conical teeth and hypodontia, are key diagnostic features. These clinical findings distinguish ectodermal dysplasia from other syndromes or conditions that affect the dentition but do not impair sweating.

Reference: Nelson Textbook of Pediatrics, Kliegman RM, 21st Edition.