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It sounds like the firmware has corrupted. You have to manually download the firmware file and use the Odin application to flash that firmware to your S3.
On your computer, download and install Samsung Kies application from here --> http://www.samsung.com/in/support/usefulsoftware/KIES/
Then download the correct firmware for your phone from here : http://www.sammobile.com/firmwares/
(In the above site, enter the exact model number of your device and click Search button. From the resulting page, download the correct firmware version you want)
After you have downloaded it, you will get a zip file. Open it or extract it and you will get a .tar.md5 file and some other files. The tar file is the firmware file.
Then follow the steps below.
Download the Odin application from here : http://www.mediafire.com/?7v7zor9d379emeg
or from here --> http://odindownloader.com/dload/Odin3_v3.10.6.zip
Then open Odin application and follow these steps below;
Put the phone to Downloading mode. To do that, turn off the phone. Turn it on and immediately hold down Volume Down, Home and Power at the same time to boot into downloading mode. Volume Up to confirm if asked.
Then connect the phone to the computer with the USB cable. A message saying "Added!!" will appear in Odin's message box at the bottom left of screen.
Click the PDA Button, and choose the .tar.md5 file (the firmware file)
Make sure Auto Reboot and F. Reset Time options are enabled. Also make sure the Re-Partition checkbox is not selected.
Don't make any changes to Odin. Click Start. Let Odin finish the process. Once it finished, it will show a Pass in the top left. P
Make sure you download the correct firmware file for your phone.
Refer this Youtube video --> https://www.youtube.com/watch?v=Ulz-1UYzHBA
(the first part of video that is the firmware downloading part might be a little different when you do it now). Please let me know how it goes.