Some of the better thought out DACs have a grounding point of some sort in order to take care of the issue that you just ran into. I am surprised that John overlooked this.
My solution is to:
Get a piece of insulated wire of about 1 meter. You can strip an old power cord of its outer insulation and then cut out one of the cables inside to give you a length of insulated wire.
Next: strip about 2cm or a thumb's width of insulation off both ends of the wire.
Unplug the DAC and amplifier from the mains. Don't just switch them OFF. You must physically remove the plug from the mains socket on the wall.
Twist the copper strands of each end a bit so that you don't have any tiny wires floating about and stabbing you in your Fingers.
Then look for a screw point on the DAC to wrap one end of the bare wires around it. You will need a screwdriver to undo a screw a little bit to do this.
Repeat the above process on a screw on the amplifier side.
Now plug the DAC and amp back into the mains and try them out. The problem should be now solved if it is an earth loop problem.
Before you do this, plug an interconnect from the DAC to the amp.
Take an Ohmmeter and measure the resistance from the case of the DAC to the case of the amp. If the resistance is zero (or virtually zero), then adding your extra ground wire may do nothing or may even make the problem worse.
Edited by Chris J - 10/11/13 at 10:43am