Leigh's disease is a severe neurological disorder that is often associated with mitochondrial dysfunction. Mitochondria are the organelles responsible for producing energy in the form of ATP through the process of cellular respiration. A malfunction in the mitochondria could lead to a chronic lack of energy in cells, which aligns with the symptoms described in the patient, such as kidney failure, lack of motor coordination, and poorly functioning nervous system.
Therefore, the most likely organelle responsible for Leigh's disease is:
Mitochondria