The staining could be from the cedar chest. Fabric should never be stored in direct contact with wood because wood contains acid. Many old quilts were stained along the folds in cedar chests.
I would try RetroClean:
http://www.retroclean.com . It may be that the staining is simply from the wood and there has not yet been permanent damage from the acid.
Incidentally, for the same reason you do not want to store fabrics in tissue paper or cardboard unless they are "archival" quality -- that is, have been treated to remove the wood acid. The same applies to photograph albums; you really want to mount photographs on archival quality paper.