Maybe your Nintendo hums because it doesn't know the words?
There are a couple of possibilities here. The NES runs internally on 5VDC. The NES power adapter puts out 9VAC. Internally, the NES contains a rectifier and a filter capacitor to convert the AC from the power adapter to DC. This DC voltage is then fed to a 7805 voltage regulator.
The Super Nintendo and the Genesis use a very similar scheme, only they rely on this rectifier and filter cap to be in the power adapter itself. So those consoles take DC, not AC.
The third party power adapters actually put out 9 volts DC. This allows the same power adapter to be used on an NES, as well as a Sega and a Super Nintendo (with different connector). When used with the Nintendo, the DC passes right through that rectifier bridge, and the filter cap does little work. Now, here's the problem. Those third party power packs are... what's the word... junk. I've seen them do weird stuff on the Super Nintendo (green bands in the picture, hum in the audio). The DC they put out isn't 'clean'. I took one of those "three in one" system power adapters apart, and I swear it looks like it was soldered by half-blind children. The component quality is abysmal. Which, is to be expected, since the things only cost like eight bucks.
The first thing I would try is to get a known good official NES power adapter and try it on your console. If one of those isn't available, the Sega Genesis 1 power adapter should also work. If you find that your console works only with a Sega adapter, and not with the NES adapter, then the filter capacitor and/or one or more rectifier diodes in the console have failed (capacitor more likely). Cheap and dirty solution - use the Sega adapter.
-Ian
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