You said that you purchased your machine used , Therefore sombody has already run the setup app. You thought that you might have a problem with your monitor cable , You never mentioned what kind of monitor you are using, I'm just speculating , is it possible that a previous owner set up the machine and entered into a preference file that the machine would be hooked up to an Apple Display Monitor (that would have a lighted switch on the bottom right of the display which overrides the power switch on your CPU) Possibly now you are now using a different type of monitor, but your computer thinks it still needs to be turned on from the monitor switch. Hope this gives you a new dirrection to look into.