The Nintendo 64 (along with the GameCube and the Super Nintendo, who share a common AV connector) outputs signals in a format called "Composite Video." Composite is an old analog standard for video output. With the addition of something called a "RF Modulator" (also known as a "RF switch") these composite video signals can be received by televisions that were only able to interpret signals from RF modulated sources, like antennas or analog cable.
The composite video spec has been obsolete for many years now, and was never a particularly popular video connection for computer monitors. Also, in the intervening years, most displays switched from supporting analog signals to digital signals. In the computer world, we went from the VGA specification to the DVI specification, and then to DP and/or HDMI.
"But wait, agent," I hear you say. "I can plug a VGA->DVI adapter into my monitor, hook it up to my PC and everything works fine, and that thing costs like $5." Yes, this is because the people who designed the DVI specification included pins to carry the analog VGA signal (DVI-D is pure digital, DVI-A is pure analog, DVI-I is both). HDMI is electrically compatible with DVI-D, just bundled with audio (and later Ethernet) signals. An HDMI port doesn't transmit or receive analog signals, so you can't plug a VGA monitor into a HDMI port by chaining a HDMI->DVI and DVI->VGA adapters. It won't work.
This intelligent connector design has led to the problem you're facing. You know you can adapt certain video signals, but what you don't know is that being able to do that is very unusual. Composite video is very, very old, and there's very little interest in modern display format manufacturers to include support for it on their new, shiny HDMI/DVI/DP connectors.
Therefore, you've got to somehow convert the composite video signal to something that your modern display can handle. This is kind of an expensive process, since there's really nothing about the two signals that is compatible. You'd have to have a piece of hardware that is smart enough to understand both standards fluently - a digital-analog converter. Think of it like a translator - a person who is fluent in two languages that will sit between your "composite speaking" Nintendo 64 and convert the information coming out into "HDMI speak."
These boxes can cost a pretty penny, and the better the conversion you want, the more they are likely to cost. It's hard to recommend one in particular, since what's best for you will vary, while the number of fakes and fly-by-nite sellers is extremely high. My suggestion would be to find a place with a good return policy. That way you can return it if you find it's incompatible with your hardware or produces poor image quality.
The other alternative in this is to purchase a monitor that has the electronics already integrated into it. Luckily, these are pretty easy to come by - just purchase a small television. Most televisions have integrated analog to digital converters. They tend to support RF in (so a RF modulator would be compatible) or even composite in. I have one TV that only has component (don't confuse component and composite!) in, but it's also got a mode where you can plug composite in to the same jacks as well.
First of all, NUS-006(01) is the part number of the N64 cartridge (please refer to Maru-chang's introduction page), so it won't help. You have to ask the seller (if possible) to provide the game serial (in NUS-NSMx-xxx format for Smash Bros) to check out the information on that cartridge.
As for European cartridges, not all games support language-switching, however as I remembered (warning: I may be wrong, so please correct me if I did make a mistake): if the second set of the game serial ends with a P (NSMP in your case), then the language can be switched to English. You may need to double check that to make sure.
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Coincidentally, I also have a 55" Vizio TV and a Nintendo 64, my favorite console of them all, in my room. For whatever reason, I was able to get my GameCube to work with the TV, but I never could get the N64 to. I just tried it again, and went through every setting I could find on the TV, but still nothing. There's no picture, but I can hear music for not even a second before it goes silent. My Nintendo 64 definitely works, as I was playing Super Smash Bros. on it just a couple of hours ago with a different TV.
All I can tell you is make sure the N64, games, and cords work by testing with another TV and then ensure that the composite cables are connected to the Vizio TV like this:
and the input is set to "Composite". If it still doesn't work, then it's your TV. You can either return it and get another brand, get another TV for your game consoles (like I have), or mod (or pay someone to mod) your N64 to output in HDMI (however, this still isn't guaranteed to fix the problem).