IPhone 5 will not connect to LTE, iMessage, OR Wi-Fi?

My iPhone 5 will not do anything but send SMS and call. No iMessage, no Safari, none of my internet-based apps work. My phone will not connect to any Wi-Fi connections either. I have done the hard reset (switching the vibrate button twice then holding power and home button down until the apple logo appears), I've turned it off and on multiple times. I have reset Network Settings as well. A friend is actually having the same exact problem and has been off and on the phone with AT&T and Apple for the last week and nothing has worked. Please help!

Added (1). I don't know how to get the sim card out of an iPhone!

Added (2). My friend who has the same problem reinserted the SIM card multiple times and it isn't working so I assume it won't work for me either.

Have you tried reinserting the sim card?

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