This is a ground loop. Small part of the current returning from CPU to PSU goes through "common ground" connection to the DAC, then through the analog DAC-amp ground conductor, causing some voltage to develop across this connection, and then back to your computer through grounding cables in the walls.

The voltage across DAC-amp ground causes a DC offset seen by the amp (likely less than 1mV). The exact amount of voltage varies in time with CPU power consumption, producing AC that you hear.

You need to eliminate the ground connection between computer and DAC (toslink, USB optoisolator, etc.).

Any external DAC will eliminate this for you.

Nope. I'm running into an external DAC and then a Rega integrated amp. Makes noise her as the bars get smaller. The noise is independent of amplifier volume, including with the amplifier volume all the way down, and even occurs with the amplier and DAC switched OFF. The noise is actually coming from the LCD.

Even decent internal soundcard does.