I do want to point out for others that google this issue and have a blank serial number (instead of having the wrong one as the OP stated), and for computers that are vintage/obsolete and apple won't touch, there have been leaked copies of the Blank Board Serializer software available on the web's more questionable file storage sites/torrent sites.
I don't think I can post direct links to them on macrumors forums, but some searching with google will probably find them.
(If your mac is still eligible for service, that of course is the preferred course of action vs trying to find the leaked software.)