Normally i run a ground back to the 4ch amp from the radio to diffuse the "loop noise". The only thing that makes me scratch my head is that its NOT there when the engine is off. There for it has to b somthin thats makin the RCA's pick up noise some where along the lines. When the engine is on. AKA a blower motor, fuel pump, ETC........
How are the RCA's routed from your HU to the amp? Are the near the AC blower? Cig lighter plug?
Also your RCA's should not be run down the same side as your power wire. Just somthin i try to avoid at ALL costs. Try the ground from HU to 4ch amp first. That should solve it. LMK and well go from there