If you have a heat gun try this, make sure the gun is on a low setting and never have it stationary on the plastic trim. Warm the trim and wipe it with a clean cloth. Warming brings out the oils in the plastic you will see a lot of gunk removed (old polish and plastic treatments) you can normally bring back most black plastic trim parts unless they are really badly stained.
REMEMBER if you leave the heat in one spot you will possibly warp or damage the trim so don't rush it, in the case of heat on plastic more isn't good