Wifi wont work in Samsung galaxy 3 even after a hard reset
Android 4.4.2 (Kitkat) was not officially released by Samsung for the Galaxy SIII.
You can search at SamMobile for your SIII (GT-I9300) and download the latest official firmware. (registration required but I can give you the links too, if you don't like to register there)
Then flash it using Odin (or similar) to get your stock firmware back.


  A private sale is free from any warranty by the seller, so you didn't even have to accept the return (in the EU at least).