Note: The cable that comes with the Switch Pro controller is a data cable and should work fine. But if it has some physical damage, then you might need to buy a new data cable.
Pair and Connect
Many users don’t know when they have to first pair the controller in order to get it to work with their PC. While connecting the USB cable, make sure you put the controller in pair mode.
Steps to pair: hold down the little button on top of the Pro Controller (used to pair the controller) and then plug it in with your PC.
Disconnect from Switch
Being a gamer, you might occasionally connect your Switch Pro controller with your Nintendo Switch and play games on that device. Since the Switch Pro controller was not designed to work on PC, whenever you connect it to PC, it connects with your Switch via Bluetooth. So all you have to do is disconnect it from Nintendo Switch and then plug it into your PC and play.
Now open Switch Settings and navigate to Controllers and Sensors > Scroll all the way to the Bottom > Disconnect Controllers.
When you’re done, it should say that only 2 controllers are connected to your Switch, instead of the 3+ prior.
To ensure that your Pro Controller doesn’t attempt to connect to your Switch wirelessly, turn off your Switch. Hold down the Power button on your Switch > Power Options > Turn Off.
Now you can hold down the little button on top of the Pro Controller (used to pair the controller) and then plug it in with your PC and it should work.
Third Party Helper
If none of the above methods works for you, then you can take the help of third party controller configuration software. The one which works best with the Switch Pro controller is BetterJoyForCemu.
BetterJoyForCemu allows Switch Pro controllers to be used with a PC. Once you have installed the application, all you need to do is run it, and connect your Pro Controller (both via Bluetooth and USB cable).
First, download and install BetterJoyForCemu on your system.

Click on locate button and it will help you to pair automatically.
Conclusion
These are all the possible methods to fix the Switch Pro controller not detected on PC. Although these would work fine, if not, we recommend you to install BetterJoyForCemu as it can help you with the pairing process. Please make sure that Windows Updates are enabled while you connect the controller with your PC, as Windows will automatically download the required drivers needed for the controller.