I was able to look at the screen and use the remote while it was lit up (although it is dim, suggesting LED brightness issues) and I noticed I have a purple bar along the left side of the screen. I'm attaching a picture. It looks like I have more than potentially just power board/LED issues. I'm currently debating my path forward as this potentially just got more complicated and expensive.

If I do get the LED tester, I see one of the voltages going to the LEDs is around 340V. The testers I'm looking at for 15-20 dollars only show up to 300V. Will that be an issue?
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I don't have an LED tester, but I have noticed the following:
With the other boards disconnected from the power board, I can get the LEDs to turn on and stay on if I short the mosfet (source to gate).
With the main board connected, shorting the source to gate only turns on the LEDs for a couple seconds.
If I ground a digital multimeter to the tv chassis and connect my positive probe to the mosfet gate OR touch it to the top of the capacitor (resistance or diode mode), the LEDs turn on.

I am not great with electronics, but I wonder about the mosfet since shorting...

I recently came across this post and the description of the problem was identical to my TV's problem. The backlight will flicker for a quick moment when powering up the TV then stay off. After reading this post, I purchased a new cap and replaced the 450V 10uF capacitor. This didn't solve my issue and the backlight doesn't even flicker when starting up now. I can do several things to light up the LEDs, so I don't believe those to be the issue. What I'm curious about now is that your image shows the capacitor near the cable going from the power board to the main board. That capacitor is 470uF 25V....