well your backlights are turning on, but after 2 seconds they turn off. So either you got a bad inverter board or you have a bad CCFL.CCFL's go, but not that fast.
If you could test the secondary winding on each transformer with your Ohm meter, we could determent which one is bad.
Well, the backlight wasn't coming on at all. Initially, after replacing the power board, the tv worked/ But, the next day, I used it and after a short period, the screen went black with just sound. After that, it would just have sound, no image.
I can test the transformer, I just don't know how to. There are 4 pins, can you instruct me on which to get the resistance? pins 1 and 3 have continuity, pin 1 and 4 are separated from everything else it seems.
You have absolute no flash of the backlights? You confirmed BLon, that comes from the main board, so it is o.k. So since you haven't got squat as of a backlight, then there must be something wrong on the PSU, not giving juice to the inverter board.
Confirm PSON, BLon, check adj pin, check main filter cap for 390v when tv is on. Measure DC voltage between VBL+ and VBL-, then the rest of the pins of cn5.
If you look at the inverter board is there a inverter controller ic on it?
Have to figure out, if the controller ic is bad, or if the PSU isn't giving any power.
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