I managed to fix this issue in surprisingly easy way. I will give you detailed information about what went wrong and what went right. I also have a few question to you.
Unfortunately I wasn't able to apply any of solutions you suggested probably because I was running windows in safe mode. I didn't try Driver Verifier though.
I wasn't able to open 'Update & Security" section in Start > Settings. Each time I did it the window closed and an error information appeared in 'Event Viewer' in section 'System' with message:
DCOM got error "1084" attempting to start the service dps with arguments "Unavailable" in order to run the server:
Section 'Windows Update' wasn't displayed in 'Control Panel'. I guess that's because I was running Windows in safe mode.
Next I downloaded Intel CPPC driver from ASUS support and removed local driver by going to Device Manager > System Devices > Intel CPPC > Properties > Driver > Uninstall. Then I started driver installation and a window appeared with error message saying 'This computer does not meet the minimum requirements for installing the software'. I made sure I downloaded driver for right device and OS version.
I also tried to remove Xbox related apps (one of them installed by me), but for every application from Windows Store the 'uninstall' button was doing nothing. However I was able to install and uninstall other programs.
What eventually worked is I opened Device Manager and pressed 'Show hidden devices' in View menu. Then I was able to see all the devices I installed earlier, in particular my controller. Next I removed a bunch of devices from 3 sections: about 15 in total (some of them were displayed more than once): 'HID-compliant game controller', 'HID-compliant game system', 'USB Input Device', 'Bluetooth XINPUT compatible input device', 'XINPUT compatible HID device' and 'USB Input Device' from 'Human Interface Devices' section, 'Xbox Wireless Controller' from 'Bluetooth' section, 'Xbox Controller' from 'Xbox Peripherals' section. I didn't remove 'HID-compliand device' (misspelling intended) from 'Human Interface Devices' though because it asked me for removal of other software.
Then I restarted my laptop and happily everything worked.
After successful reboot, I reinstalled Intel CPPC driver, removed 'Xbox One SmartGlass' and 'Xbox 360 SmartGlass' (the former was installed by me. It may or may not have been involved in the BSOD issues).
I also noticed that a few of the devices I removed were back in Device Manager so I removed them again and I also opened 'Devices and Printers' in Control Panel and removed my controller from there.
I rebooted once again and everything was as it should be.
Could you please explain what do you mean by
Only 4 Windows Update hotfixes installed. Most build 14393 (1607) systems have more than this.
I'm trying to keep my OS updated by visiting 'Update & Security' in Settings and installing all available updates regularly. Is there anything I am missing? I checked my Update history and every update that failed to install was successfully installed later. And is word 'hotfixes' relevant here or did you mean 'updates' in general? I searched internet for more information and people had different understanding for that word.
You also mentioned I had a 'Tilt Wheel mouse' driver installed. I think removing this driver would help me solve my initial problem (that lead me to adding/removing my controller repeatedly), but I can't find it anywhere in Device Manager. Could you please advise me where I can find it and how to remove it?
Edited by bsodman, 06 January 2017 - 04:42 AM.