dvdljns:
Hello and welcome to the forums.
In so far as I know the security or lack of security on a wireless network should not keep it from showing up as an available network connection, however; if the Wireless radio is not broadcasting a SSID (Service Set Identifier) then it will not show up. So you may want to reset your router to factory defaults by using the reset button inside the hole on the back of the router. Be aware that if you do choose to do this and are using a PPPoE connection from your ISP, you will probably need to re-enter your username and password for the WAN side of your router. And I would highly recommend configuring some type of security for your wireless network, at least WEP but preferably WPA or WPA2