I'm not sure what you mean by adding a resistor since the 7N50 is a 10V 7A 50W MOSFET which is as close (slightly higher) to the original as I could find. I deduced from some of your blogs that you are a repair professional, which I can assure you, I am not. I'm a hands-on, learn by trial and error, school of hard knocks kind of newbie to electronics repair. I've had a few basic electronics classes but never finished because the theory behind how everything works wasn't what I wanted to know. Of course, now I believe that if I knew how the circuits were supposed to work, then I would be able to figure out why they did not work. By trade, I am a natural gas compressor mechanic so this is not my area of expertise and therefore I am grateful for all of your expertise and knowledge you are inclined to share. Just my two cents...
So, back to the subject at hand... I just ordered a replacement board for the time being to further diagnose the problem at hand of no backlight (and until I learn more on how to repair the broken one and then I will have it as a reference for voltage checks and such.) However, when I installed this board I got the same results from before I blew the MOSFETs. The set will shut down with a 1x blink indicating lamp issues. If I force it into service mode, the LCD only briefly blinks on but the set won't power off on a fault as before.
So I disassembled the LCD display. All ten bulbs are lighting but nearly all are discolored on the ends and several were a pink/purplish color. Any ideas on how to proceed? Where should I investigate? Is there a voltage check on the inverter output? A way to test the lamps? The inverter circuits won't switch on unless there is a load, correct? Nor will they switch on if the current/voltage draw is too high, correct? And this is why it's shutting down the backlight, correct?