Are you talking about the chest that's surrounded by lava? If so, I will tell you that it has nothing to do with the amulet or the hint given by the ice elemental.
There are multiple ways of getting to that chest. Some things to think about:
- the door to the chest conveniently allows you to see through it, meaning you can drop items and target spells in the room.
- lava doesn't magically and instantly kill you, it just applies lots of fire damage.
- there are ways of moving chests around...even from a distance.
- don't you think there's something odd about those statues outside from where you teleported in...
As for the king's treasure room, make sure you are wearing the correct amulet (I don't think the ice elemental explicitly states this, but it is the royal guardsman one, not the winter amulet), and also you have to be standing still in the right spot for a few seconds before the game acknowledges it.