You didn't tell me the cable between MB and power supply before. Normarlly power socket is on MB. I think either the cable or your power supply have issue(assume your new MB is good) so that can't power on the MB.
The battery use a different path to provide the power which is indenptenly the power supply. If you have a good battery, no matter your power supply/cable is bad or good(even some parts broken on your MB for power supply path), it should power your MB up.
With a good battery, you even can try boot your old MB. As I said your old MB broken parts may along the supply path but not on the battery path. You said before your MB die, you saw the message system can't find power supply, that imply that power supply path has trouble but battery path should be good since at that monment your system still running, it powers from battery. But evently your battery drain out so the system is dead.
