What ever experience you have, there is always chances for missing something, that might be a very small problem or big !
So It's always better to go through the basics once or twice or even thrice before getting in to advanced troubleshooting .
It might be weird to ask you to do the following steps, but missing any of the following might cause an issue that you experience now :
1 ) ESC Throttle calibration : there is no option to calibrate ESCs with Naza, so you have to calibrate each ESC individually or all together with a parallel wiring harness .
2) Check Motor rotation direction , Propeller directions and Propeller Balance , ...
3) Mount flight controller almost at the center of the frame very tightly - It should not be mounted loose.
4) Check motor connections : For a NAZA unlike most other flight controllers , M1 is the front Right motor (CW), M2 is Front Left (CCW) and M3 is back left (CW) and M4 is Back right motor (CCW) .
5) I assume you are using the FS-T6 , Make a new model memory with Airplane/ Glider settings . Or reset an existing model memory. Assign any of the switches that you are comfortable with to Channel 5 (which will be used to change flying modes).
5) Connect NAZA to PC and calibrate everything as usual (Also check for any F/W updates) .
6) Make sure the main battery and Transmitter battery are fully charged .
7) Now try to take off - and not the issues if there is any.
If the battery monitor of NAZA is giving false alarms , you can avoid the Naza PSU and power NAZA directly from the ESC BECs (I am still not clear which battery alarm is triggering in your case! is it Main battery or Radio battery
)
Please Post your complete setup - incl. motors, ESC , battery etc... and also update with any Issues after going through above procedures .
Good luck