Thank you very much for your reply! At your suggestion, I put my old GPU (an EVGA GTX 570 HD) into my system, and I was able to power it on with no issues, the display working fine. I borrowed my brother’s system, verified it was operational, and then swapped out his GPU (can’t remember what it was…) with the problem 290. It exhibited exactly the same behaviour as it did in my system, refusing to power on when the 6 and 8 pin ports are plugged in, but powering on just fine (albeit with no display) when they aren’t, the 290’s fans even spinning in this instance.

I will send off an email to the RMA department. Thank you once again!