Enabling WEP or WPA encryption in the router's settings should be straightforward and not involve going through the main setup process again.
However, the PC(s) will have to re-connect to the wireless network, i.e. you should delete any existing profile, scan again 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 will then have to enter the encryption key that matches the one set up in the router before the connection will succeed.
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In the Wireless Adapter's software, when the "Available Wireless Networks" are displayed, is there perhaps an option to set the priority, so that your own network can be set as the top priority?