Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
First we can reset your iPhone and see if it works or not. Press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot.
Note : Power button is the button you use to turn off your iPhone or its screen. Home button is the round button at front bottom.
Please let me know if that didn't work, so we can continue troubleshooting.
It is possible that software of your iPhone got corrupted during the update. We can try to activate it using your computer. First download and install latest iTunes on your computer from here --> http://www.apple.com/itunes/download/
Open the downloaded iTunes installation file and follow the onscreen instructions to install it. After installing, open iTunes. Connect your iPhone to your computer. iTunes will recognize it and ask you to activate it. Follow the onscreen instructions. Let me know how it goes