If your Galaxy S4 is not connecting to Samsung kies then the reason behind this problem can be listed as:
1. Kies is not installed properly
2. Corrupted USB drivers
3. The data cable is not working
4. Defective phone/computer
If the problem is related to software, then it can be solved easily but the hardware-related issues need to get fixed by the technician.
Way to fix Galaxy S4 is not connecting to Samsung kies: (Software related issues)
First connect your phone to computer through a data cable. If a message is reflected saying that USB or the device is not recognized, then the problem is related to USB drivers. So you need to reinstall the driver by going to Device manager and update the drivers from there in online. If you have not installed the kies or if the installation is not done properly, then install it again. You can go for the connection troubleshooter by the following steps. This will help you to handle the issue if your Galaxy S4 is not connecting to Samsung kies.
> First reboot your phone and computer after closing the kies and disconnecting the phone from computer.
> Now launch kies on your computer and click on tools.
> Choose Troubleshoot connection error and click on start.
> This process will install the drivers, in case they are not present in the computer, or else it will be reinstalled for corrupted drivers.
> Click on yes if any warning message is shown for any installation.
> Now connect the phone with the computer after troubleshooting to find out if it is working.
If you have recently updated your phone, then nothing can fix the issue until you uninstall and reinstall the kies. However, if the problem occurs due to the broken data cable or defective phone, computer then get a new data cable and contact with the technicians for phone and computer hardware problem.