I'm with wayne, need to see some good, clear pics, and some close-up shots if possible Daniel.
That's a great tip Keith, now noted in my memory cells, the 'little grey cells' as Poirot would say.
I'm a little puzzled that turps should attack the plastic, unless it's a really strong %, and even then, it shouldn't really do much, apart from possibly a slight etching, which would make 'fresh' plastic a little matt in appearance. Are you sure it isn't cellulose thinner? That would certainly dissolve the plastic.
EDIT:- Nearly forgot, IF this should ever happen again, pour milk over it, followed quickly by a strong solution of detergent, such as dish-washing liquid, in water. The milk won't cure the problem, but it should start to halt the process, whilst the detergent will separate the oils in the turps/thinner, making them inactive, and then it'll be fairly easy, if a little soapy, to rinse off any resulting mess.