You don't need a Pentium, a Celeron will do, it will save you about 25 bucks.
Why 8gb of ram? 4gb will do. Can cut cost there as well.
I run that exact corsair psu and I'm not a large fan. There's a total of six 8pin ports on the back, but you'll need one for your cpu. Contrastly, the evga p2 platinum 1200 has six dedicated vga ports and two additional for cpu. Also that cost estimate is crazy. Where are you getting that? I paid 230 for my corsair and 220 for my evga.
Out of curiosity why the two different gpu models?
Also, not listed but you'll need a hd. There's a sandisk 120gb ssd for about 60 bucks on Amazon just for info! I run it. Great quality.
Oh. AUD. Got it. Nevermind what I said about prices. Too lazy to delete on mobile.
You could try that. Something else I would try is isolating that card. You say the first five cards work, so you can safely and reasonably assume that the motherboard PCI slot, riser card, and PSU connectors for your main card are working properly. Take the five out (just unplug) and plug your 6th card in to the main PCI slot using a known working riser card, known working VGA rail on the PSU, etc.
Then you can see if it's a defective card or not. If it still doesn't work I'd say card, if it does work then you've at least eliminated that. Then I would focus on power issues if it's the 6th addition that fails your system (as opposed to that 6th CARD specifically).