... Have not tested under load. ...
I would try to test under load, and feel if the connectors on the ATX adapter ends (either the motherboard side or ATX side) are getting hot. This may seem like a little thing but this could be something as simple as a continuity problem.
Also do you have another ATX power supple to try? Some of the older or cheaper supplies have issues with proper voltage or noisy voltage. I don't know how sensitive the A3000T motherboard would be.
I also suggest looking for blown Caps on the A3000T. The old power supply may have damaged a cap or two when it blew.