I wish the OP good luck. I've tried getting my PC to recongnize my S3 with no success (this all started after upgrading to 4.3). I've tried everything. Well, I've not yet sacrificed any chickens, but I'd give that a shot if it would help. I've done the cable thing, the driver thing (even older ones), the Kies thing, the booting into safe mode thing, I've tried other PCs, hooking the USB cable up with the screen on and off, hooking the cable up with the phone on and off. I've trolled every Andriod forum available and nada. Having said that... actually my PC does recognize my phone 'cause I can see it in Device Manager. It's Windows Explorer that won't recongize it. I forget off the top of my head who it was, but a really helpful member of this forum tried in vain the help, but even he had to give up. Yes, I've wiped the phone and started from scratch. All that did was use up a bunch of bandwidth putting all my apps back on the phone.
If you figure out something I've not yet tried... I'd be happy to give it a shot 'cause I'd like to root my phone. I'm tempted to give AirDriod (or similar app) a try, but I've not found anyone who's used one of those apps to root. If that'd work, I'd give it a try but I don't want to brick my phone in the process.
BTW... there's tons of posts on the net about this problem. Many people, like me, have yet to find a solution.
Good luck...