|It can be made to work, Get your wireless router and temporary connect it to your computer via wire. When you are into the routers configuration screen disable DHCP and NAT. Set the routers base address to an address within the existing range but out of the DHCP scope of the existing router.|
Configure the wireless part of the router. Use WAP-PSK if available in preference to WEP for security.
Once you have your computer communicating with the wireless router plug in the existing cable from the other router the one of the LAN ports on the existing router. Restart the wireless router and re-boot you computer and it should all be working.
I would inform the householder of what you intend doing. There should be no objection but he might not like the idea of a wireless router strung onto his network.