I have a Dell Inspiron 1525. After shutdown the screen remains white (lit up) and not black even when not connected to any power source or showing any indication of connection rot battery or AC source.

Try opening up the back cover and removing the heatsink. You will more than likely find that it is packed with dust. Clean it out using a can of compressed air. I am sure that the white screen is a warning that the CPU is overheating. I had the same problem with mine and gave the heatsink and other components a good clean out. To date I have not had the white return.