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This is because the Power Mac G4 1.25 GHz has file-sharing turned OFF.Also the Network of the G4 can see the macmini, but the mac mini network doesn't show any other computers.
System Preferences > Sharing > Personal File Sharing -- make sure it is checked off.
Is your router a wireless one? Both computer should be connecting to the same router, not different routers, even if they're all interconnected.