Many years ago I had a riding buddy who showed me his trick to making his old KDX look like it had new plastic (at least from a few feet away anyhow). Since that time I have used Plastic Renew to restore my plastics when I've laid my bike down and scratched it up. If used properly, Plastic Renew does a really good job. But it costs around $17.00 a bottle and requires a fair amount of time and a bit of work if you want good results. If your plastics are not too scratched up and they just look dull and old, for less than half that much money you should give this a go.
What you do is get a bottle of Mop & Glo (the stuff that you use for vinyl or linoleum floors). First clean the plastic really good using a non oily type of cleaner. Don't use Plexus or SC-1 as they have silicone in them. Then take a paper towel or whatever and apply a light coat of the Mop & Glo. Be sure to use slow smooth strokes when applying to avoid bubbles. It should begin to dry in a few minutes. After a little bit, apply another coat or two. Depending on how bad the finish was will determine how many coats you need to put on.
Anyhow, it should look much better and you'll be happy to have your bike shine again. I've tried this on my old chest protector too and it worked beautifully. I don't know if it will give the desired results on transparent plastic (the see through stuff) but on solid colors it works great. You can also go right over graphics too as it helps shine them up as well.
If for some reason you feel like you made a big mistake, don't panic. Just use a little bit of ammonia and water to strip it off and you're back to where you started. Now you can step back and admire your handy work. Good luck.