I've never heard of a Unibody 'Collector's Edition' MacBook, it probably doesn't have a serial number because it was never an official Apple computer.
I gotta give you props for that one. 😀 If you really want it badly, you can try the Genius Bar. If not you can always find the serial number under your MacBook on the base.
I have the same too after upgrading my RAM and HDD, I no longer have the serial number listed under software.