I've only ever seen it applied to Component, though, perhaps that has not always been the case.
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I've never had any problems using an NES with an HDTV with A/V cables. The RF adapter doesn't necessarily give the best signal, but it's worked just fine for me, too.
I've never had a problem using composite cables with an NES on an HD TV. I've had three different models of TV over the years, with no problems. No display issues, or input lag. I've had a Westinghouse, a Panasonic, and a Samsung TV. However, I HAVE had an issue running my SNES or GameCube through S-Video and an Elgato capture device on my Samsung. I receive a similar error to what you are seeing with your NES. My guess is that you have one of the rare TVs that just doesn't work with HD. Do you have access to another HD TV that you could try this with? A friend's maybe? It could at least rule out any issues with the NES, not that I would assume there are any.
That being said, NES looks pretty bad on HDTVs, even with composite audio/video cables. Genesis looks pretty bad as well. I still use my NES and Genesis on my HD TV for convenience, but when I feel like getting the best picture possible for the equipment I currently have, I just go with a good ol' tube TV. You can output SNES to S-Video, and if your HDTV takes that hookup, it looks REALLY good. Not RGB good, but good.
classic model NES has two ports on the side for those cables. a single video and audio jack, yellow and red.
I've at least confirmed this is supposed to work, I guess. :/
This HDTV was from this year. Vizio D32h-c0.
Check if you can change display modes while AV input is selected. Maybe your TV is trying to apply some kinda of video adjustment that is incompatible with the NES signal. Try turning off any "features" your model might have. You might also try getting some kind of tech support for your TV model. Have you confirmed the cord/nes works on another tv?
I'll have to do that later, too tired tonight, plus work soon. But I'll give it a try eventually