So you are saying that your molex connector got burnt ( or your PCI connector got burnt?)
Can you take a better picture to show what is broken and where is it burnt?

Which motherboard are you using? If it is H81 (as you are having 6 RX480s per mobo so my guess is that it is H81btc pro) then do not power your motherboard through molex power connectors. If you power that molex on motherboard it will burn due to some weird problem.

I use a lot of those boards and there is nothing wrong in powering those with a simple sata connector and PCIe to the USB riser. Make sure that you are using only one sata port per USB riser. DO NOT use sata extender (used to power multiple HDDs) to connect multiple USB risers. If needed use Molex to sata converter but dont put too many connections on one line.

...Waiting for the pictures ...

I use EVGA 550W to power mobo and sub risers (all 6 of them) and
http://www.ebay.com/itm/94-Platinum-1200-Watt-Power-Supply-Kit-for-GPU-Open-Rig-Mining-Ethereum-ZEC-/371643723687 to power all my graphics cards through PCI-express slots.
Its a platinum rated PSU so wastage of electricity is wayy too less.