I would clean with soap/water, then wipe with a generous amount of isopropanol (it won't hurt anything but will dissolve residual oils/wax). Then see what you got. If you use a plastic cleaner like Back to Black, rub it in with a toothbrush and let sit a few minutes until it is almost dry...... then apply again over the first and while wet, wipe any excess off. Should improve it to some degree.
If not cured, wipe again with isopropanol, and if you're feeling brave, wet a cloth with acetone and wipe the whole surface. Feeling super brave, find a bit of MEK, it will dissolve/etch plastic and paint. You may be able to find a carb or brake cleaner that has it as a component.