Im fairly sure that GnR mostly used Les Paul's into Marshall's most of the time
but, if your after the sound as it appears on that YouTube clip. firstly, keep in mind that its horribly compressed (in the size reduction codec sense). one way to get a similar sound would be to use a poor quality distortion pedal, one that adds a fair whack of white noise. i have a zoom that gets close to that sort of thing. or perhaps you could run some pink noise into another channel and gate it with the gtr signal and mix that in.
also, ive heard some small practice amps (like 10 or 15W) driven really hard used to great effect to get a boxy, squashed and lo-fi distorted sound.