You're right, this isn't exactly the right forum, therefore I will keep it as short as humanly possible. You should let the G4 do the work (description is for Leopard, but should work in Tiger as well). On the G4: System Preferences > Sharing > enable File Sharing. If both the G4 and the iMac are on the same network (and the WiFi router is set up to allow the connected WiFi devices to communicate), the G4 should show up under 'Shared' in the iMac's Finder sidebar. If that doesn't work, in the same System Preferences pane, enable Internet Sharing as well, sharing from Ethernet (even if that's unplugged) to computers using Air Port (provide a 'Network Name' under AirPort Options that you will recognize later). Also note the 'ComputerName' on top of the panel. You will now see a new network called 'Network Name' in the iMac's Wifi network list. Connect to it. Then in the iMac's Finder: Go Menu > Connect to Server, and type afp://ComputerName._afpovertcp._tcp.local
For questions please PM me at [email blocked] since I don't want to abuse this Tender resource, and I know the topic can be quite complex.