Step 1: Zellweger syndrome belongs to the peroxisome biogenesis disorders, caused by mutations in PEX genes needed to assemble the organelle.
Step 2: The result is a failure to form functional peroxisomes, so the defining feature is reduction or absence of peroxisomes.
Step 3: Without peroxisomal beta-oxidation and plasmalogen production, very long chain fatty acids accumulate and myelin formation suffers, giving the hepatic, renal, and severe neurological features.
Step 4: The other organelles do not fit: lysosomal disease gives storage disorders, mitochondrial disease gives energy-failure syndromes, and a nucleus-less cell cannot survive.
\[\boxed{\text{Peroxisome}}\]