Final answer:
The most likely impaired cranial nerve in the scenario where an infant did not blink when their eye was touched is the trigeminal nerve (CN V), which is responsible for the sensory component of the corneal reflex.
Step-by-step explanation:
The scenario described where an infant did not blink when their eye was touched suggests that the cranial nerve responsible for the sensory input of the corneal reflex might be impaired. This reflex involves both a sensory and a motor component. The sensory component, which carries somatosensory information from the face including touch to the cornea, is mediated by the trigeminal nerve (CN V). The motor response that induces blinking is controlled by the facial nerve (CN VII), which innervates the orbicularis oculi muscle. Therefore, since the child did not blink when their eye was touched, it is most likely that the trigeminal nerve is impaired in this scenario.