Accessing S/N of G3 Beige MiniTower through software.

Question

Is there any software than can fetch me the serial number of my G3 Beige MiniTower? 
I've got this Frankenmac (G3 Beige upgraded to G4 trough PowerLogic ZIF chip) booted into native MacOS 9.2.2 and connected to my mini-network through Ethernet.  The native MacOS 9.2.2 Apple System Profiler doesn't bring up a serial number, and the Tiger and Leopard System Profilers can't read the G3 hardware.
Just curious—and hoping not to have to disconnect and take apart the G3 Beige MiniTower just for this purpose. 
Thanks in advance.
Software overview
    Serial number:    Not applicable
    Mac OS overview
        Finder:    9.2
        System:    9.2.2  US
        Active enabler:    None
        QuickTime:    6.0.3
        CarbonLib:    1.6
        File sharing:    is on
        Multiple Users:    Not installed
    Note: No startup disk was selected.
Memory overview
    Disk cache:    8160K
    Virtual memory:    769 MB
        Used on volume:    FrankenMac_HD9
    Built-in memory:    768 MB
        Location            Size           Memory type
        J3          256 MB   DIMM
        J4          256 MB   DIMM
        J5          256 MB   DIMM
    Video memory:    16 MB   
    External L2 cache:    Not installed
Hardware overview
    Machine ID:    510
    Model name:    Power Macintosh G3 series        <<<===
    Keyboard type:    Apple Extended Keyboard
    Attributes:    Audio/Video card
    Processor info:    PowerPC G4        <<<===     <<<===
    Machine speed:    533 MHz
    Nanokernel version: 2.27
    Nanokernel pool extends: 0
    Nanokernel scheduled CPUs:

Answer 1

Thanks a bunch for that info, Allan!  I would have never guessed.
That means the S/N in my machine is long gone, as neither one of its two SCSI internal drives shows a S/N.  Both HDs appear to be nominal 18 or 20 GB, so neither one is the original.
I was just curious about the manufacture date of the machine, but since that model was only produced for some 14 months, from mid-November 1997 through late December of 1998, it wouldn't make that much of a difference.  It has the last ROM version (Rev. 3: $77D.45F2).  I bought it second hand in 2002.
Given that it has the PowerLogic 500 G4 ZIF processor, the date of manufacture seems even more academic now.  
Thank you again for the authoritative reply.