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I'm not exactly sure what you're trying to ask, but it sounds as though you are unable to connect to your home router yet you are able to utilize another connection. If this is the case, then it is likely you are simply experiencing problems with your router or gateway and not your computer.
The easiest way to remedy this issue is to perform a factory reset on the router. There should be a small button that you will need to hold down for at least 20 seconds in order to restore the device to default settings. Most are set to automatically broadcast the default SSID (the name of the WiFi network) which you will need to select from your wireless network menu on your computer after the device concludes the reset process. Simpy plug in the default password and you should be able to connect to the internet.
If that doesn't work, the device is faulty (e.g. a bad radio) and will require replacement. Or you may just need to pay the bill :P I've done this before myself - hah.