I don't think I have the complete picture here - your home Wi-Fi network shows up in the list of SSIDs, so you select it and it prompts you for the password, which you enter, and then what happens? It shows 'Connected' but you don't really have an Internet connection, or it just doesn't connect?
Which Security level is the router using - WPA/WPA2 PSK? (If it's using a different security level you may want to change it - some people have had nothing but trouble with the other selections available on the router.)
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