Hi,
Have you tried taking the 'DIM' lead out of the plug to the inverter, and applying, say,
3V to the DIM inverter board pin, to see if this brings up the backlights?
Possible the DIM from the main PCB is causing the problem.
Has the inverter PCB a ribbon cable to the LCD control panel?,
I have had problems with this type of arrangement where the control PCB was causing
the backlight problem.
Good luck,
John