SIRIUS Radio static ?

I am having an issue with static when radio is played through the FM frequency in my car. I am aware of all the issues with radio frequencies and the antenna being a cause but here is the kicker, when you grab the AC power cord which powers the radio it sounds perfect, no static when I let it go static comes back. Although this is not all the time it is very irritating when it does happen. This is a new radio with a brand new power cord, I replaced my old cord on my old radio and it did not help so I thought it might be the old docking station connection. Is it possible that it might be an issue with my cigarette lighter or other interference from something else? Can I buy something or rig something up so I don't have to touch the cord to eliminate the static ? Ground it somehow ?