Here is a simple schematic which will help you understand what's going on:
o-gs/dji-hardware-schematics
ESCs are telling the motors to beep if FC (which is on the sub-board marked "CENTER" on the schematic) cannot talk to them.
If one motor beep, that usually mean this specific ESC was damaged or its copper path to FC was broken.
If all motors beep, that means the connection to all motors was broken (ie. the solder joints which hold the
FC sub-board are cracked), or the FC is dead.
If you look at the schematic, OFDM board has direct connection to Gimbal Top Board. This is why the damage on ESC Center Board does not affect the video. OFDM and gimbal must be working correctly.