For plastic I would be tempted to try Brasso or Silvo liquid metal
polish..! Use a very soft cloth and rub in a circular motion over the
entire screen it can be done with Duraglit or Sivaglit this is a metal
wadding but the liquid form is best - I can not comment on other brands,
if in doubt try on some spare plastic.
There are no doubt many rebuffing kit's specially for this purpose -
this be may is your best option.
For glass, I got deep marks out of glass TV xcreens with Chemico... a
grinding paste that you use on car pistons, you just gotta rub and rub,
glass is harder and takes longer.
... no genie come out but your knackered afterwards I can tell ya'. The
secret no matter glass or plastic is to use a small circular motion,
obviously you need to conentrate on the scratched area as well as the
entire screen... don't want it concaved do we like Hubbles lens.
I do believe there is some special stuff that you can fill the
scratches with up but I can not comment nor tried any of these.
Why not take it to an optician.... WHAT...!!!!
Well, you see glasses are always getting scratched and specticles can
be glass or plastic.. some opticians have on-site 'despener & repair
unit's'.
...you'll find some giving naughty gestures, some may appear friendly
and yet one of them just might be friendly... not too friendly mind.
*You do need to be careful*... it may be coated with an antiglare
coating or even a scratch resistant coating - just like they use on
specticles.
So inspite of making a specticle of myself, gotta admit.. a method in
my madness though
Davy