i never paid close attention to the green key symbol on my 04 civic because when i start the car it usually goes away. But just a little while ago the light stayed on and didn't go away. Is this something I should be concerned about?

 

welcome to the forum. the green key symbol being on would mean the car is immobolized ( sp) you sould not be able to start the car due to security system.
sorry don't know much more. the light should not be on after starting