The image you are seeing when light is flashed upon the tv indicates that the video board is functional and so is the power supply board. It definitely indicates a problem with the backlight. When you say you replaced the inverter boards do you mean you have replaced both master and slave?

If you can hold a flashlight up to the screen and see the picture, then the only thing that is not working is the inverter.

If the inverter connector on the main controller board has DC voltage, then the only thing that may be faulty is either the inverter or the wiring to the inverter.

If there is no DC voltage to the connector, only in that case you may have a faulty PSU or a faulty main controller board.

There is not much to play around , parts must be tested, and the faulty one replaced. All the technician must do is following voltage from main board connector to inverter, or backward to PSU, depending if there is voltage on main board connector to inverter or not.

Also ensure that all the connectors are in place, and check connection between slave and master inverter board.

If there is no voltage on main controller, then test bridging the +5V control line from main board to PSU that turns on voltage to the inverter. If bridging the line the inverter turns on, then the main controller board is bad.

All test and repairing must be done by a trained person.