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#1 In the router, did you try to change the SSID?
#2 In the router, did you try to change the channel?
#3 In the router, you are using wireless security? For example, WEP OR WPA.
#4 You do not have any cell phones or cordless phones, near wireless equipment?
No idea of how to do those thing in the router, the brand and model of the router will help.
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Cell phones operate in licenses spectrum, and the frequencies they use are not the same as the frequencies used by WiFi.
Most WiFi is in the 2.4 Ghz band. That is unlicensed spectrum, available for a number of uses including cordless phones. The point is interference in the 2.4Ghz band from other Wi-Fi Networks in the area, as well as cordless phones isn't unusual.
So you may have to try different channels until you find one that works. It may be that none will work very well, in which case there isn't much you can do about it.
So it is entirely possible that the cordless phone is interfering with the wifi.
WEP security should not prevent your WiFi devices from finding your network, however if you lack the password, it will prevent you from using the WiFi network.
Depending upon your Modem/Router, the instruction for changing your wireless setup vary, but start by going to http://192.168.1.1 and logging into the modem/router as administrator, preferably from port 1 on the modem/router. There should be a 'wireless' tab, click on it, and a menu should open up to allow you to change the channel, SSID, WEP password etc.
Anyway, if you have a WiFi enable devices, it should be able to see the network, even if it cannot connect to it unless the signal is being interfered with by another device in the 2.4Ghz band.