Hi Aston,
Periodically Xbox 360 controller may not work on Windows 10 because of the outdated or unmaintained drivers, and if that is the reason, your Xbox 360 controller is not functioning properly, the best way is to uninstall the already existing driver and allow the Windows to install it again. Click a Windows 7 option. Since the Xbox 360 controller doesn't have Windows 8 drivers available, you'll use the Windows 7 drivers that correspond to your version of Windows (32-bit or 64-bit). If you aren't sure of your operating system's bit count, you can check your version of Windows. If you’re using wireless Xbox 360 controller, set up install your Xbox 360 wired controller on Windows 10. But, you should update the drivers for wireless receiver timely, or may be your Xbox 360 controller will not work on windows 10.
Based on the description, I am sorry to know that you are getting an error “unable to install driver software' and the device manager says 'this device cannot start (code 10)'.
I am sure this could be frustrating. Please be assured that we are here to guide you in the right direction.
The Code 10 error pertains mainly to hardware and device driver issues or to compatibility issues between hardware drivers and additional software that is installed in Windows. Therefore, we recommend that you troubleshoot these issues by focusing on device drivers, on device configuration issues, and on hardware compatibility issues. You might need to update the chipset drivers and the USB controller
For more information, visit the following link.
Description of Code 10-related errors that Device Manager generates in Windows-based computers
Let’s follow these methods and check if it helps.
Method 1: Perform clean boot and check
To help troubleshoot error message, you can start Windows Vista or Windows 7 by using a minimal set of drivers and startup programs. This kind of startup is known as a 'clean boot.' A clean boot helps eliminate software conflicts.
How to troubleshoot a problem by performing a clean boot in Windows Vista or in Windows 7
Please note: After the troubleshooting, make sure to boot your computer to normal mode by following the step 3.
Refer the following articles and check.
Set up your Xbox 360 controller for Windows
What to do when a device isn't installed properlyYou may also get in touch with Xbox support and check.
Xbox 360 Controller Driver 64 Bit
If the issue persists or you have further questions on Windows, please do not hesitate to let us know. It is our pleasure to be of assistance.