Add me on Snapchat!!
Ok if your Snapchat is working on 3G but not Wifi, then this sounds more like an internet connection problem than an issue with the Snapchat app.
Most obvious thing is to double check that your Wifi is turned on.
Then after that, check that your router is turned on and transmitting correctly.
Sometimes it is worth turning it off and on again...
Still not working? Have you tired browsing the internet on your phone on Wifi? If that IS working, but Snapchat isn't, then maybe it's a bandwidth issue... Aka the action Snapchat is trying to perform is more than your currently available bandwidth can handle.
You also have the options of restarting the Snapchat app, or resetting the phone, but I really don't think the app itself will work on 3G but not Wifi.
I fixed it by going into snapchat settings disabling notifications then enabling it. Sent my self a snap see if it worked and it did.