Just solved a very simular Problem! Is the Battery full? If you are lacking Charge? Hook an external power suply on the + and - poles of the Battery. You might just want to do this anyhow since that way you can make sure you are not facing a Battery Problem. Now install usb Drivers on your PC, deaktivate Kies. Get Odin, Hook up the Phone to usb, then apply Power. Now quickly: Power, Home, Vol. down.
This should get you into OdinMode. Wait for the Drivers to insall and so on....
Without the USB Kabel atached this phone would not go into Download Mode!
What a fun dance! S3 ist up an running again.