@feedyourbiology this "I tried unplugging the main board from the power board (based on what I found on the forum here) with a hope that the backlight will turn on," does not work for Sony:-) Check CN6601 for the STBY voltage of 3.3V if you do not have that voltage, it is your power board. Do not rely on the single 12V Remember that your power board supplies the STBY voltage to the main board. The mainboard tells the powerboard to turn the rest of the TV on, once it receives signal from the IR board :-)
If you can, post some good clear pictures of the board (straight down will be perfect) so we can try and figure out what is going on with those.