The primary reason the Peloponnesian War started was due to rising tensions and rivalries between Athens and Sparta, specifically related to their competing interests and the power dynamics in Greece. Among the options you've provided, the most accurate answer is:
Sparta and Corinth became jealous of the wealth and power of Athens.
Athens had become a dominant naval power and was wealthy due to its empire, particularly after its victory in the Persian Wars. This growth and influence created fear and jealousy among other city-states, particularly Sparta and its allies, which led to the eventual outbreak of the Peloponnesian War in 431 BC.