What is the most fundamental purpose of investigation?

The most fundamental purpose of investigation is to determine all of the facts important to render judgement on a matter.

In a criminal case this involves determining if a crime has been committed, the party responsible for the crime, if they acted alone and if not whom they acted with, and all the relevant facts needed to bring the case to a successful trial. Paying careful attention to evidence that might prove the innocence of a party or conclusively prove guilt.

In a civil case the purpose is to determine exactly what occurred and how and what factors may place responsibility for the loss or injury on any party.