If this is one of those soft touch surface coatings, you may be stuck. These were very popular on consumer electronics and in cars a decade or so OK, but they degrade over time and become very soft/sticky in the end. As Mikesmith29 says, the best thing is to try to clean it all off and accept the underlying plastic finish (which may or may not be nice, given that it wasn't intended to be exposed), or remove the part, clean it and get it refinished by painting or otherwise. Google "soft touch plastic" for more.