Johann, the OP asked how to reinvent Police Quest, not remake it. There is a big difference between the meaning of those two words.
My opinion here: The problem with having a non-violent Police game is that the majority of the commercial gamer market is made up of teenage boys with short attention spans and limited intelligence. So the only games that keep them happy are simple click and shoot games like FPS games where no-intelligence is required. If you die just reload from your save game 30 seconds ago and keep on trying until you finally succeed. They do not have the attention span to actually work at a problem to solve it. And judging from various message boards, most of them do not have the basic literacy skills to actually understand an adventure game properly.