The ethernet ports in each room should lead back to a patch panel which might be in the garage or somewhere else inside the house. You run a short cable from the patch panel socket to the router LAN port. The working telephone wall socket for the wifi router should be here also.
I'm assuming that your internet access is working. (When you connect the router DSL port to the telephone wall socket, do the DSL and Internet lights come on?)
Are you using the TPG voip phone service?
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Just like what @david64 said, you may need to check if there's a patch panel near the telephone wall socket in the garage. If there is, then you need to connect an Ethernet port from the modem/router LAN port to the patch panel ports.
You may contact your landlord or the previous owner of the house to check the setup of the internal Ethernet cabling on the premises to confirm if what you desire will work.