I should preface this by saying that I'm a relatively brand new driver, and I know next to nothing about cars.
I've got a 2005 Chrysler Sebring, and I've noticed just today that when I put the ignition into whatever mode it is that lets me control the power windows and listen to the radio without actually turning on the motor (I turn the key slightly forward -- I'm assuming this is not the accessory mode as when I turn the key backward, the radio comes on but the power windows do not...) the check engine and oil pressure lights come on and stay on. However, when I turn the engine on, the lights go off. All other diagnostic lights are off before turning on the engine. It is only these two that stay on until I turn on the engine.
I checked the oil level just to see if it may be off, and I can't be 100% sure of the actual oil level due to my driveway being not being properly level... but it looked to be just slightly down.
Is this expected to happen given that the engine is off? Do the diagnostics only work when the engine is running?