From the view of an Engineer well versed in power systems, seeing just that one PCIe connector burnt is highly suspicious.
Either:
A) The board was powered by just that one connector. If so, of course it fried...
B) Very bad sockets in the PCIe cable feeding it. I do see that there is no solder fillet around the pins where they join the board. I will assume that there is good solder on the backside. Lack of a bead on top is not good but not conclusive.

One problem with "B" -- if all 3 connectors were being used, the other 2 should have picked up the slack resulting from the poor connections. Remember: All 3 of the PCIe connectors are in parallel. In no way could there have been enough current through them (bad connections) to burn it and the 2 good connectors show no signs of overload at all eg, turning brown.