No, the noise does not change if the cable is wiggled. It sounds like I either need a device that reduces (filters/masks) that noise from the USB jacks of the computer box, or I need a different source of music if I want to eliminate that background noise. There is a super hub called Vaunix hub that sells for $200 that is worth looking at - I have an inquiry into them asking if their device is designed for this type of noise elimination.

Obviously most desktop computers are not designed to be low noise music sources. I would like to find a way to overcome this reality short of getting a new computer or moving everything over to my slightly quieter laptop.