This sounds like an open earth ground circuit to me with your description. Check your house wiring and see if it checks out proper. You can get a plugin device for this if you don't have one. Which leads to the second possibility, the new unit is not properly grounded internally. This could either be a design flaw or a bad/missing earth ground connection.
What would cause noise (ground noise?) when touching the volume control and tone controls?
I have a new preamp that I recently hooked up and I'm getting some interference or what may be ground noise but I only hear it when I'm physically touching the metal volume knob and tone controls. When I touch the metal top of the case in addition to the knobs, the noise will subside. Just looking for ideas to help isolate the cause. I think the case itself just isn't grounded sufficiently.
I have tried new power cables, RCA cables and plugging into different outlets with no change.