Livey,
From my limited experience i havnt found many products that will do wonders for plastic or perspex windows but depending on there condition i used to use tooth paste to lightly polish old motor cycle windscreens. They didnt come up like new but anything left outside for 20 years wont, but there was a great improvment. This worked the best as its a miled abrasive but like all cleaners try in a small area first.
Hope this helps,
Cheers Pete