ND2901/ND2730/ND2700 does not turn on with USB power, if the battery is empty.
ND product charge internal battery during the power off state. You can see RED LED lit during the charge.

If the internal battery is fully discharged, the battery goes into LOCK state to protect itself.
If that happens, the battaery can be charged but cannot output power.
So ND2901 does not turn on without external power.

This LOCK can not be unlocked by USB charging.
It can be unlocked by AC power adapter or by plugging out the internal battery from the unit.

As soon as you connect AC power to ND2901, it is immediatly unlocked.
Or, if you unplug internal battery then plug it again, then it will be UNLOCKed.
To remove the internal battery, open the top cover. Un-fasten four screws, then you can remove the top cover. You will see the internal battery and battery connector. Remove the battery cable from the PCB then connect again. Then it will work again.

You can use any AC power adapter as far as following condition met.

1. The size of connector
Outer dimension : 3.5mm
Inner dimension : 1.5mm(1.3mm acceptable)
(*)See here for the connector size
--> https://en.wikipedia.org/wiki/Coaxial_power_connector

2. The voltage of adapter
ND2901 / ND2700 : 5V
ND2730 : 12V