03 X5 Sleep Issues

[03X5]

All: Brand new to the forum and I sure hope you can help. Our 2003 X5 is killing the battery after a couple of days. Seems the radio does not go completely off (you can turn it on anytime after you shut down the car, open doors, close doors, whatever). When you punch off the on/off switch, the time remains in the screen and there is a faint glow where the radio station and/or BC computer display was....I was told by the BMW dealer the radio was faulty and not allowing the car to go to sleep....has anyone else had this issue and is there a way to trouble shoot to see if it really is the radio? Thanks! BTW, basic Business CD, no Nav, no DSP.