No internet while on WiFi is no fun. Let's work on resolving all issues. Run in safe mode http://goo.gl/dxV1i and test. If issues do not occur while in safe mode, you have a 3rd party application conflict. No easy way to identify such conflicting app. You will have to remove all 3rd party apps and install one at a time and test between installs to identify bad app and remove for good.
A corrupted system file may also cause the issues outlined in your post. Do a factory reset http://goo.gl/tbjkt and test before installing any 3rd party applications. Keep us posted.
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