Pathos Verdes III had two sons, whom he buried in two separate locations in Pandora's Temple. In order to traverse the temple, one would need to find their corpses, and take their skulls. Their skulls then function as keys. Kratos finds the bodies of both sons, and takes both their skulls. The first skull is used to unlock a doorway into the second Ring of Pandora, and the second skull is used to drain out the water in the third ring. Verdes III was ingenious in his idea to implement skulls as keys, but he most likely did this because of his growing insanity.
When Kratos was on his mission to stop Ares' reign of terror, he was told that he would need the power held within Pandora's Box to defeat him. He used the skulls for their purpose, leaving the bodies without skulls. The Temple was then left without anything to stop mortals from reaching the box (including Kratos).
In the Cliffs of Madness, several deceased soldiers' bodies are found. It remains unknown how those soldiers got so far without having taken the skulls from the sons' corpses. It is possible that this was a mistake overlooked by the developers.