When you add a conversation to an NPC, it should just work (unless that NPC is hostile, or cannot be reached, or some other confounding factor).
When you add a conversation to a placeable - say, a trapdoor, a box, a statue - the game doesn't automatically know what to do with it. To make that placeable act like an NPC and talk to the player on click, you need to add a script.
x0_startconv - Add to the onuse slot in the placeable properties. Makes the placeable start its default conversation (i.e. the one in the conversation slot) with the PC on use.