Help Home Wifi problems

I have an LG Optimus Elite, and when I got it everything worked fine. I powered it off, and the next day my home Wifi said it was connected to the phone, but some of my apps would not work. Only Skype and the browser would work, but Gmail, Facebook, Google Play, ect. said there was no connectivity. The date and time was also automatically set to January 7th 1980, at 12:00 AM when I turned it back on.

I reset my phone to factory defaults, and everything worked again. But when I powered it off and on again, it did the same thing. I've had multiple iPod Touches that worked on my internet, and my friend has an Android phone that connects perfectly fine, as well as tablets and multiple laptops.

I'm not sure why it partially won't connect after powering it on and off, but if this persists, I will have to send it back. I have tried resetting the internet from my phone, and from the modem, but nothing has worked.

Please help!