I second the Novus polish suggestion. Novus #2 does wonders on smooth unpainted plastic surfaces. You don't even have to completely clean it first. I found an early 70's high-end 19" Zenith B&W in the trash a couple years ago with a white plastic cabinet. It was *filthy* dirty and heavily scratched up (nothing too deep though). A few minutes with Novus #2 (and a little elbow grease), and it looked practically brand new! Really amazing. Now, on that pebble-grained plastic often found on TV cabinets, it's not quite so effective. [The toothbrush suggestion works great though in that situation] I'd also not recommend it on painted cabinets, since it will probably remove the paint/coating. ...But on solid-color smooth plastic surfaces it's hard to beat.
Novus polish should be harmless to plastic, since it's really just an abrasive paste. Follow up with plain water (not soap), and you should be fine.
Tip: Novus polish also works great on scratched-up cloudy-looking plastic headlight bezels on cars. Also for reparing scratched CDs. ...Now how much would you pay? But wait, there's more!
