So I actually got the GPU from one of my friends, and it worked fine in his build, so I can verify there's no problem with it internally at least. Unfortunately, I don't think he has a spare PSU though.
I went and doubled-checked just now, and the connections seem very secure to me for both cables on both ends. Trust me, I was really hoping this was just a cable connection problem too haha
I assembled my PC and tested it with no graphics card. Mobo RGB lights worked, fans spun on, and keyboard received power. Everything seemed good.
A few days later, I inserted the graphics card (GTX 750i) and powered on. Everything is still fine but no display because I forgot to plug in the...