Have you tried running wireshark or running a tcpdump on the ubuntu box and looking to see what's going wrong. It's obviously 'hearing' stuff as there is an ARP table and a load of RX packets, is your DHCP not providing a suitable gateway so the Ubuntu box can get out to the internet (via the router) but is unable to get out anywhere else....
Ideally, if you have ssh access to your router, you could tcpdump from there and pipe it via netcat to a machine running wireshark & netcat and filter on the IP addresses you are interested in.
ETA: What's the router IP?, your gw is 192.168.1.254, if that isn't your router IP, then that might be your problem - though odd if it's DHCP, unless you've configured separate DHCP for that mac address from the router?