I think the pilot implied that Trudy's murder triggered Monk's obsessive–compulsive disorder (OCD), which let to him having to leave the police force.
But the episode Mr. Monk and the Marathon Man contained a flashback, showing him at a younger age:
Young Monk wasn't able to run because he obsessed over his uneven shoelaces (after that episode the writers stuck with the idea that Monk already showed compulsive behaviour as a child).
I remember wondering if that was a goof, because if he had OCD before he became a cop, how did he manage to pass the police academy?
Did the show ever address how Monk got through police academy with his OCD?