could be the clock module itself is just screwed. The clock is supposed to dim when the lights come on. Maybe you have a short somewhere, but you might want to try replacing the clock. You still have yours from the old car? If power to the whole car is being disrupted when the car is shut off, then the clock on the stereo (assuming you have one) should get reset when you turn the car off too. If it isn't the problem is just local to the clock module, try replacing it if you have a spare.