Should be About This Mac>More Info>Hardware Overview
Is it not shown there? If not it probably indicates that the logic board has been replaced and the S/N was not loaded. There should also be a S/N sticker somewhere on the case of your iMac.
Note an iMac 4,1 can't be running Mac OS X 10.4.1. 10.4.1 does not equal 10.4.10, and is less than 10.4.11 as well. 10.4.4 is the minimum system for such Macs.