Kyran you are NOT alone... I was so ******* frustrated by this purchase.
I have the exact same problem, exchanged them and had the same problem on 5 different computers. These things are made with barely any barrier against noise from a PC. The technician claimed their $12,000 setup didn't have this problem so it must be my machine. Well guess what... I BOUGHT A $100 DAC! I'm on a budget and wouldn't use a $100 DAC with a $12,000 system if I had one!
They have to know that the kind of person who is going to buy this is using a basic computer setup yet they blame your computer for giving off too much noise. Well out of those 5 computers one was an Apple iMac. Is Schiit trying to tell me that a Modi isn't supposed to work with an iMac?
I ask any Modi owners using regular computers to listen to this file and not hear squelching at the beginning and end.
http://www.audiocheck.net/Audio/audiocheck.net_headphoneshaker.mp3
What I ended up having to do is buy one of these ADuM4160 USB Isolator boards.
http://www.circuitsathome.com/measurements/usb-isolator/ - Info
I ordered mine from China (Teralink) on eBay for $25, which took a month to get and then it died and had to wait forever for it to be returned and replaced. I suggest you get one from Oleg at Circuits at Home:
http://www.circuitsathome.com/products-page/usb-interfaces/adum4160-usb-isolator-board-populated - $48
You can even build your own with one of his packages if you're capable.
You'll also need the correct power adapter and a USB A Male to USB B Male, shorter the better, adapter which can be tricky to find. I bought my USB adapter in a set like this:
http://www.usbgeek.com/products/usb-adapter-set - i didn't actually buy it from these guys though.
It's not 100% gone, doesn't run at 24/96 most of the time, and sometime requires reconnecting but it works pretty good. Enough to not anger me every time I reach for it...
The only thing left that I haven't tried is to see if I have the same problem with higher impedance headphones.. not that it would matter much. I originally bought the Magni/Modi set and then got a couple of lower impedance headphones HD 598's and SR 60's because of great deals.