Problems when trying to connect XBox One S Controller to PC
I have three recommendations to solve your problems.
#1
Since it is one of the features of the new Xbox One S controller to be able to connect wirelessly to your pc, I suggest you
- restart your controller by pressing and holding the home button for 6 seconds
remove the controller from your pc devices. Go to Settings > Devices > Bluetooth. Then you can select the controller and then select "Remove device."
then follow the steps in this video Use Bluetooth to connect your Xbox One controller
#2
The alternative & best way to connect a Xbox One controller to your PC is to buy this: 
It doesn't cost much, you can get for less than $20 on Amazon, and trust me my friend when I tell you it will make your life easier. You simply plug it in the USB port of your pc and connect your controller wirelessly. Magic! Also it supports up to 8 controllers simultaneously as well as 4 chat headsets and 2 stereo headsets, so it's definitely worth it in my opinion!
#3
If you need to use the controller urgently and the first solution did't work, just use a micro usb cable to play temporarily until you get the problem fixed.
It looks like this: 
Hope this helps!
I think I found a solution. My wife had the same problem after the firmware update, so I fixed it that way:
- Plug the controller by USB on the PC
- Uninstall the driver of the contriller in the "device manager"
- Unplug the controller and turn it off
- Turn it on again and pared it by bluetooth again
After these steps, it should work.