I doubt it is the board.
Or the new card.
So it would leave when putting the new Psu in, forgetting to connect a power supply to the board.
If the system does not post, or power up properly, or the bios does not produce a single beep to say everything is working as expected.
Check the Atx 24 pin block, and the eight pin block are connected to the motherboard.
And that the extra power feeds from the psu are connected to the Pci-e 12v power point on the R9 cards.
May I ask what brand of power supply you replaced the old one with?
And how many watts it is.