Did you try testing the phone on a different WiFi to see if it will connect to that one? Say at a friends or a free public one? I say this because if the WiFi works elsewhere, then you can download any needed updates when using a different WiFi.
Now, if your phone won't access WiFi anywhere, I would start to wonder if there is an actual problem with the phone. In this case, I would then recommend going through to step 6 listed above. BUT BE SURE you back up the personal data (contacts, photos, videos, music, etc.,) to another device, say a computer, before doing it as all data will be reset on the phone and it will wipe everything that is on there now. Should that not work, then there may well be a physical problem with the phone...