While watching, the screen went almost black—just a faint, gray glow. (I think the sound continued). I turned the TV off, then back on, and it worked for a few minutes before going dark again. I let it rest a few hours, then it worked again for a few minutes before emitting a whistle/buzzing sound (like a July 4th rocket) that went from a high pitch to a low pitch over about 5 seconds—then it turned off completely.
Now, when I touch the on button, the dim red light pulses 3 times, then goes off and the screen glows a very dim gray.
All of the cylindrical capacitors look very clean. Nothing oozing out of them, no bulging, etc. However, there’s a funny-looking green part (about 1/2 inch diameter and 1/8 inch thick— I’ve been told it’s a “varistor”) that’s green on the sides, with a bubbly, yellowish area in the middle. It’s a little sticky on the outside, like something’s leaked. The bubbles inside the clear, yellow area make me think this is the part that made the noise as it “cooked.”
Digit-Key support offered a part, based on the "TVR 14621 820W" printed on the outside: https://www.digikey.com/en/products/detail/littelfuse-inc/V385LA20AP/1009520
It looks quite different, but great if it works, and would only cost about $5, including shipping.
Should I give it a try?