One (likely) possibility:
The logic board has been replaced. (Highly likely on almost any iBook G3. I remember reading at the time that maybe 75% of iBook G3 would need replacement. Not sure how accurate that turned out, but I replaced a bunch, probably 30 or more in the little shop where I worked when the iBook G3 was current.)
And, the replacement logic board never had the serial number installed (which uses the "Serializer" utility provided to Apple service.)
Don't think you can add the serial number after the logic board is put into use.
Rodan52 post is accurate, of course, but simply tells you what the serial number should be. If there is no serial number burned to the ROM on the logic board, then you will see what you see now, -0000, or simply blank...