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Novus 3-step polish is generally great for this. I've used it on numerous pieces from my collection with excellent results, including Power Mac G4s, iBook clamshells, my Cube, and this CRT. It's pretty easy to use; you just work your way through each of the three bottles until you achieve the desired outcome. It leaves the acrylic feeling smooth and slick, I love it.
Just be aware that it can be a bit tricky to remove it from any seams/gaps that it makes its way into. For this reason I always try to avoid getting too close to panel gaps, inset logos, etc.
You could try to use a buffing wheel but I always found doing it manually to be fine.
Below are some images of my 17" ADC CRT Studio Display before and after a disassembly and cleanout + polish. As you can see, it worked wonders. It wasn't able to totally remove all of the deeper scratches, but it vastly improved the condition of the case, almost looks new again. Cleaning out the inside also helped tremendously.
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