I believe that the camera's default IP address is 192.168.0.20, so unless your router is serving that number range on the LAN it won't see it.
Example - in many Mac systems the router may be at 10.0.1.1, serving addresses like 10.0.1.n -
Assuming that is the case, can you try (temporarily) connecting the camera directly to the computer, and setting the computer to be manually 192.168.0.1, with "router" set to the camera ip, and mask 255.255.255.0. Then start a browser and put the camera ip into the address bar. Then you can set the camera ip to whatever the router needs - of course it will stop being visible with this hookup, so next, go back to normal router connections.