Why was the murder of Laius never investigated?

The murder of Laius never received proper investigation primarily because it was overshadowed by the more immediate and pressing threat posed by the Sphinx. At the time of Laius's death, the Sphinx was terrorizing Thebes, presenting a challenge that demanded the city’s full attention and resources. The people were largely focused on the Sphinx's riddles and the dire consequences of its rampage, leading to neglect of Laius's murder. This urgency created a situation where the investigation into Laius’s death was effectively sidelined, as the city prioritized resolving the threat that was directly affecting their safety and survival over investigating a past event that seemed less critical in the moment.