Even though there's power it could be a bad PS, you need accurate voltage measures or better yet, a spare PS. If after replacing PS problems remain then most likely a bad mobo.
It's a long shot, but try re-seating everything. A PCI card not fully seated could be an issue. Hope it gets fixed. Dead PC is no fun. (Unless someone is looking to upgrade).
Oh don't matter, not going to enter in details, but you are good to go and install that PS, unless mobo connectors don't fit.