There is always hope for those who still have problems, and the problem IS solved by the switch to USB debugging and then turning it off, but you have to be a little careful about what is going on. So, in addition to what was posted above by Tenjo:
First, I will assume that you are running Windows 7 64 bit, since that is the most common these days. Post if you have anything different.
Please do EVERYTHING here, in order, and don't skip any steps "because you already tried this".
So, first up, disconnect your phone from the computer.
Next, run Kies, and make sure the loading screen shows the copyright is through 2012, not 2009. A new version of Kies was released a few days ago. To check, in Kies, you can click on Help, and then "check for update" to make sure or to download the new version. If you install an updated version, if it tells you to reboot the computer at the end, DO IT, don't skip that step. Help and "Kies Information" should read: 2.5.0.12094_28 if you are fully up to date on Kies.
So, you have the latest version of Kies. With the phone still unplugged, the main screen shows the top option of "Connect a device to use all the Kies features", and there is a "button" labeled "Troubleshoot connection Error". That is what you want to do. Click it, and let it update the Kies driver on the machine. At the end, it will probably tell you that you need to reboot for the changes to take effect. DO IT, do not skip that step.
So, you have rebooted, possibly twice now. So, there is something to note for this next step that is somewhat important. When you first connect a device, before Windows 7 even looks on the local computer for drivers, it checks "Windows Update" to see if there is a newer driver. The problem in this case is the driver that Microsoft may try to pull down will override the driver that Kies would be trying to use. The trick then, is when you click to see the driver install status, there is a SMALL thing you can click on that says to skip checking Windows Update. You WANT to skip it, and if you just let it pull down the drivers, who knows what will come down.
So, that is what you need, connect your Galaxy S3, and make sure you skip the Windows Update part of the driver check process for all elements that show up. If it fails, or only one of two or three drivers goes in, unplug once it gets finished, unplug the phone, plug it in, and repeat, again, making sure you skip the Windows Update check for drivers. Now, reboot the computer yet again, just to be sure things are set. This reboot may be the only part of this where you MAY be able to skip.
So, phone still plugged in, fire up Kies, and see if it works. If it works, great, you are set, if it does not, there is still a good chance the next part will do it, and it follows what Tenjo posted.
So, now, it isn't working yet, so unplug the phone, and follow what Tenjo said about settings, developer options, and enable USB debugging.
Once you have enabled USB debugging on the phone and have saved the settings, plug your phone back in to the computer.
You will now get the driver install window again. As before, DO NOT INSTALL DRIVERS FROM WINDOWS UPDATE.
And as before, once it is done installing all the drivers(if you have to unplug from the computer and re-plugging it in to get whatever failed), try running Kies with USB debugging still turned on.
At this point, Kies should be working properly, and you SHOULD notice it connects nice and fast to Kies, no slow check for the phone in Kies.
If Kies is still having problems, either you did not bypass the Windows Update check for drivers, or you have: A bad USB port, try another on the machine, preferably on the other side from the one you have been using, OR, the cable you are using to connect your phone is having a problem. Just because a cable works for charging does not mean it will work for sending data to/from a computer.
If all is working with Kies now, you can unplug from the computer, and turn USB debugging off. Then, connect to the computer again, and it will try installing drivers yet again. As always, DO NOT INSTALL FROM WINDOWS UPDATE.
Once done, plug in, and Kies should be working with the phone NOT in USB debugging mode.
I have been fairly verbose here to let all of this sink in. It may not be as easy to read, but it hopefully gets the point across not to skip steps when trying to deal with this issue. Older versions of Windows from before Windows 7 don't really make use of Windows Update, so many have never had to deal with Windows Update being preferred over a locally installed driver. I hope this helps.
fraNK
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