Your computer is showing it's connected to the Wifi router all right, but perhaps the router isn't connected to the Internet.
If your connecting the Ethernet cable directly to the modem and resetting it, bypassing th erouter and then getting online, fine that's good.
If your connecting to the router directly and getting on the Internet fine, it means the router is connected to the Internet.
If the last one is true then likely what has occured is your DCHP lease is expired because your computer doesn't have the right time and date as the router, it's showing a good signal but your not connecting.
Open System Preference and check the date and time and set it to update to Apple's time server for your location.
Sometimes Apple's time is off, as third party routers get their time elsewhere and sometimes the two don't match and thus DCHP lease is expired.