I cannot assess whether DOJ would take the case, as that's something you'd need to contact them directly about. As for a private civil rights claims, the answer is most likely not. Only very rarely are lawsuits successful against police for failure to investigate, and it's usually only where police do something affirmatively to facilitate the crime or where they've assumed some specific duty of protection regarding that particular individual. Schedule a consult with a NYC civil rights lawyer for a full assessment.