If you are connecting to the router "wirelessly" from your *OLD* laptop, then the router must already be set up correctly and you should have no need to access its Setup page (at 192.168.0.1) from the new laptop.
Having said that, if the new laptop was connected to the wireless network, it should be able to access the router.
Have you actually "Connected" to the wireless network? In other words, have you run the wireless adapter's software, scanned for "Available Wireless Networks", found and highlighted the one that matches your router's SSID (network name) and selected the option to "Connect" to it? Once "Connected", the wireless adapter should get its IP address by DHCP from the router and you should have network and internet access.
There is a difference between the Wireless Network Adapter and Router communicating with a good signal and "Connecting" (as in "logging in") to your Wireless network.