Nice PC. The issue probably isn't the mobo. The Gigabyte Z68X should be fine. CPU should have no effect. What PSU are you using? You didn't skimp on the other parts of your system so I assume you have a decent PSU.
If you're going from:
PC -> USB to E7 -> RCA to Magnum -> Headphones
Then I'm pretty stumped why the noise is being picked up on the USB cable, assuming there's nothing wrong with the cable. I'm also assuming all your gear is properly grounded.
The only suggestion I have is make sure you're not using DirectSound for music playback, and instead try using WASAPI output through Foobar and see if that helps. Foobar automatically claims exclusive mode when using WASAPI, so you won't be able to get sound through anything else until you stop playing music on Foobar.
Let us know if that helps at all. If you plan on getting a good DAC, I'd just return the E7 and get something like a AMB gamma2 (if you don't want to build one yourself, you'll have to commission one), and use coax or Toslink for it. There are a lot of good popular $300-500 DACs nowadays.
From looking at your mobo, it looks like you've got digital out. In my experience, most DACs don't do USB very well. The latest generation of Gigabyte onboard implementations are good, so I don't think you need a PCI sound card to solve this issue. If you have a PCI sound card laying around, I'd plug it in and output through that, straight to the Magnum, to see if it solves your problem.