Firstly, if you are connecting a Laptop "wirelessly" to a Netgear router for internet access, this has *NOTHING* to do with your desktop PC - it is totally independent of the PC which won't need to be running.
You need to "Connect" to the wireless network. In other words, run the wireless adapter's software, scan for "Available Wireless Networks", find and highlight the one that matches your router's SSID (network name) and select the option to "Connect" to it. You should be prompted to enter any WEP or WPA encryption key and, 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.
If a default WEP or WPA encryption key has been set up in the router's wireless security settings, there may be a note of the key in a label on the underside of the router.