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Yeah if your not seeing the anything even before Windows starts loading drivers then theres pretty much nothing you can do at the OS level to fix it - other than using it to apply firmware updates. Try it without the HDD connected just to see if you can see the error it spits out when no bootable media is found.
EDIT: Though some variations of GPU and monitor might not work at displaying anything at BIOS level at all - IIRC the DGM ones often don't like an AMD GPU.
Re-install windows?.
OP, try disabling the on board and then boot into Linux off a USB stick or CD.
Worth a shot I guess but looks like its gonna have to be an RMA job to me. Given the number of people I know out of those who have bought 290s that have the blackscreen/redscreen issue and had to RMA I'd honestly buy a 780/ti if your gonna have it setup in a loop.