Does your power supply have a third wire?

If no, things become simple, just order another MB and try.

If yes, you need consider a little complicate. Because you try it on a different type NB, as I know, such as the Dell power, I can only say your power supply voltage/current may be good, but the third wire function may be broken. --Your said your earlier MB prompt can't find power supply--that is exactly the problem in your power supply.

Depends on BIOS, some NB need that 3rd wire provide the power-id to decide if it boot or not. Some don't.
If the MB can't detect the power-id then it need the battery to boot.

I learned this because I have a MB the power-id detect function fail(same as power supply power id function broken). it won't boot unless I have a function battery insert.

For your case, your battery total empty. So it is possible your previous (ordered) MB is good, but your power supply missing the power-id and your battery can't provide any current. That result you can't turn on your NB.
If all above are true then order another MB will not solve your problem.