Was it on an IBM Aptiva by chance? There was an app called Kids' Room that was included with Aptiva systems, which was basically an interactive desktop and program launcher. I remember there being a bunch of little mini games/puzzles, and there were characters who would talk or do certain things if you clicked on them.

I too enjoyed this as a child (if it is indeed what you are referring to). I recall pixel hunting for what seemed like ages, just trying to hear all of the noises or figure out what objects I could interact with.