Abarim Publications' online Biblical Greek Dictionary
The verb πειναω (peinao) means to be hungry and, apart from its parent noun πεινη (peine), hunger, is of unknown pedigree (albeit not without similarities to ποινη, poine, retribution or vengeful satisfaction, from which comes our English words pain and penalty).
Hunger is a sign that one's basic necessities are not being met, and heralds the death that is inevitable if the hunger is not assuaged. Hunger often comes accompanied by διψος (dipsos), thirst, and both are characteristics of πτωχεια (ptocheia), destitution, the polar opposite of ελευθερια (eleutheria), freedom, which is the purpose of the Gospel of Christ (Galatians 5:1). This helps to explain how Jesus could claim that he was "the bread of life; he who comes to Me will not hunger, and he who believes in Me will never thirst" (John 6:35).
A life of eleutheria is a life of completion (שלום, shalom), not a life of not having to eat (Luke 24:43), but rather a life devoted to the absorption and application of an abundance of hitherto unrelated elements: a permanence at the point of intersection of a great many continuums (Revelation 21:26).
Our verb is used 23 times in the New Testament, see full concordance, and has no derivations.