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Depending on your router, "access control" may be enabled. With this setting, only devices that have been connected previously and had their MAC address stored are allowed to connect. Go through your wifi settings and make sure an option with a function like this isn't enabled. On a Netgear router, you'll find it under Wireless Settings -> Access Control. Also make sure you haven't run out of IP addresses, in case you shrunk your allowed range for any reason.
Along with my WPA2-PSK password protection, I keep Access Control enabled as well so even if a new device has the correct password, it cannot connect to my network without me adding it to the router's list.
PS Vita Won't connect to home wifi - PlayStation® Community Forums