Tapshi, does your 737NG have a normal battery and an Aux Battery?
Looking at the Maintenance Manual for the single battery type NG, there is a Remote Control Circuit Breaker (RCCB) between the Hot Battery Bus and the Static Inverter. The Standby Power Control Unit (SPCU) opens this RCCB if the battery switch is selected OFF (unless the Standby Power switch is selected to BAT)
On the dual battery NGs (i.e. those with a regular battery and an Aux Battery), there is also a "DUAL BATTERY RCCB". It has different logic from the normal RCCB. However, looking at the wiring schematics, power from the Aux Battery has to go through both RCCBs (in series) to get to the Static Inverter. On the dual battery type NGs, the logic for the normal RCCB is the same as the single battery type NG.
I can't see how you can get power to the Static Inverter (with the main busses dead), if the Battery switch is not ON, or if the Standby Power switch is not in BAT.