As you said when there is no backlight the problem is either inverter or power board. In some case the main controller board may be responsible.
You need to test the parts to find out what part is responsible. Testing is done tracking voltage from PSU to inverter. Voltage to inverter is usually supplied by the higher VDC line from PSU. Here broad description of how to test the three
parts: Before proceeding...
The TV can be repaired at component level or replacing boards, depending on your skills and experience. If you want to repair at component level, after diagnosing the faulty board you test components and circuits individually. In that case to test inverter in full you will need an oscilloscope to read the phase of inverter AC section (oscillators or IC must be tested).
Note: If Inverter has voltage out to CCF lamps, then the parts mentioned above are OK, in that case you have a faulty LCD panel. The TV is usually not worth repair as the LCD panel is expensive. LCD panel faults are not common.Here replacement parts for most flat panel TV models:ShopJimmy.
See also: PartStore