There is a problem we come across every once in a while. Blown ground or grounds on the head units. What leads me to believe you may have this problem is that you get a loud hum when both your RCA plugs are not connected.
Blown grounds on source units are caused when the power grounding on the amplifier is poor or gets interupted for some reason. At this point the amp gets it's power ground through the RCA sheilds and the source unit. Now since the current draw from the amp can be hundreds of amps the foil on the printed circuit boards in the source unit can not take that kind of load and what happens is that the copper foil on the pc board of the source unit burns and creates a open circuit. If the RCA outs on the source unit have seperate paths to ground on the Printed circuit board then lift one or the other and you get a loud hum. If both are blown you get low output or very loud hum or whine, all depending on what ground paths are left available.
You can tes this by using a multimeter and checking for continuity first between the grounds on the RCA jacks on the source unit. You should get a short circuit indication. Next check the continuity of each RCA jack ground to a known good chasis ground. Even if the RCA ground on the source unit is isolated from chasis ground most amplifier audio grounds are not. Again you should have a near short circuit indication between RCA and chasis ground. If you do not have this indication in any of these tests it means that the grounds on the source unit have opened up and that needs to be corrected.
Another way to test this is to use a different source unit, such as a walk man or such. If the wnine goes away then the problem is in the sound card.
If you find that the grounds are blown then before replacing or repairing the unit, you need to thoroughly check the ground path from the amp to the battery and make sure that it is and remains a solid connection.