I suspect your hum is caused by the new interconnects. You mentioned that "If nothing is connected to my amp, it's quiet when every thing else is cut off. If I connect the balanced ICs I get a low volume hum through the speakers."
Since you didn't mention what they are, how long they are, or if they are running near any power cords, then we'll go through the whole list.
First, are they shielded? If not try replacing them with ones that are known to be shielded.
Second, are they longer than a meter? If so, is there any way to reduce the distance between pre-amp and power amp and use shorter ones?
Third, are they running next to any power cords, wall outlets, amplifiers, subwoofers, tv sets, flourescent light fixtures or any other device that has a magnetic field around it? If so, can you move the interconnects to achieve more distance from the magnetic field?
Progessive Electronics make a tool for the telephone installers called a 200B Inductive Amplifier; it's about $35.00. It has a magnetic pick-up at one end and when placed next to a wire with an AC signal or current flowing through it, the 200B will allow you to hear the signal (or hum if it's AC power). With it you can find the source of your hum very quickly.