The G4’s out of the picture, I’m afraid. To have music in both your rooms (without moving the iMac) you’d need a Roon endpoint in the living room. This is where the network comes in. Ideally, you’d have Ethernet cable running between the two rooms, along with an unmanaged switch or switches in the mix. However, with the right WiFi network, it should be do-able via WiFi. What specific model is your AirPort Base station, and what’s your WiFi signal like in the living room?
Have a look at this KB article:
What are referred to as “outputs” in the article are essentially what I’m calling “endpoints.” Given your current hardware, I think you want a RoonReady device that has Ethernet and/or WiFi in and USB out (in your case to the Bel Canto DAC). Note that Ethernet in could be by means of a WiFi router (maybe an AirPort Express in your case), a WiFi access point with an RJ45 jack, or a mesh router.
There are a lot of these kinds of endpoints available, ranging from quite inexpensive (e.g., Raspberry Pi, Cubox-i) to mid-priced (e.g., the Sonore Sonicorbiter SE) to relatively expensive (e.g., the Sonore microRendu and ultraRendu). (The cheapest endpoints tend to involve more DIY effort to set up.)