Congratulations on your find. I wouldn't change out the motor and light if they work. Even if they don't seem to match, they have probably been on your machine for a very long time and have become part of her.
There was never any serial number information for the JC series on the Singer site. The JC machines were made in Saint-Jean-sur-Richelieu, Québec, Canada, in 1948 as Charlee mentioned.