I'm with Redlyr re: bad ground, and I was going to suggest check the antenna ground, but if the problem is with the CD player too, that kinda rules that out. So, this is going to be a bit of work, but pull the stereo out to access the power wire to the head unit, and feed it directly from the battery, using an inline fuse. Also ground the head unit directly to the battery Neg. terminal. Just run the wires out the car window for now, for this test. See if the problem is still there. This way you can determine if the problem is in the stereo itself or in the car's wiring. This is a tough problem to diagnose, but we'll find it.