Ruled by Acrisius, its throne went to Diomedes directly from his grandfather, the  organizer of the Seven Against Thebes.
One prince of this kingdom was a shepherd who either died of a snake-bite in the heel or was killed by the Nemean Lion.  Shortly before her death, Alcmene undertook a journey from this place to Thebes, but died en route at Megara. This place  was ruled by a king who prevailed in a womb quarrel with his brother, to whom he gave rule of Tiryns. This place enjoyed  a prosperous five year reign under a man who broke Aeneas's hip by throwing a stone and won the (*) chariot race at  Patroclus's funeral games. This kingdom was jointly ruled by Proetus and a man who was killed by a discus by Perseus years  after locking up Danae in a bronze tower. Ruled by Acrisius, its throne went to Diomedes directly from his grandfather, the  organizer of the Seven Against Thebes. For 10 points, name this Peloponnesian kingdom whose inhabitants gave their name to the  Greek side during the Trojan War.
One prince of this kingdom was a shepherd who either died of a snake-bite in the heel or was killed by the Nemean Lion.  
Argos [accept Argives, I guess]