You should reflash your stock firmware and root again via odin. You can also use framaroot or towelroot to root the s3.
https://towelroot.com/ - just download, install and 'let it ra1n'
http://forum.xda-developers.com/apps/framaroot/root-framaroot-one-click-apk-to-root-t2130276 - same as above: install and choose exploit, then reboot.
If the above does not work try the below.
First off all you should download the proper root-file written for your phone (e.g. cf-autoroot) and odin 3.09. Activate the developers options by hitting the build number seven times and enable usb-debugging and unknown sources - then put your phone into download mode (vol-, home and power buttons) and make sure your phones usb drivers are installed to your pc. Then turn off samsung kies and your antivir, because they will cause problems. Now start odin as an administrator and connect your phone via usb. There should be a blueor yellow com:0 box lighten up. Press the pda button and select the unzipped content from your cf-autoroot file. Do not touch the ticked boxes on the left side!!! Press start. Your phone should load the data and restart by its own. The rest happens by itself.
Flashing a firmware is done the same way as above with the following exceptions:
- you dont choose the autoroot file. You choose the firmware.
- you can download clean and official firmwares at sammobile.com
- flashing can take up to 40 minutes
- i do not like samsung devices