If you bought Windows 10 on-line through Microsoft or it came preinstalled you should have what is called a digital license and the hardware should be recognized and activate automatically. That is what SHOULD happen but I'd store the registered key code to be safe. Still, let's hold off on formatting for a while.
First off please don't run any of those 'fix my PC' type packages. As you can see they can wreck havoc. Since a reset can save data and settings I can see Defender still failing but don't see why it should fail on a clean install.
Before we do anything I assume, without Bit Defender installed, that you have gone to settings/Update and security/Windows security to confirm that Defender is in fact disabled. If there is a green check mark on Virus and threat protection Defender is actually running and it may just not be set to show in the Notification Area by the clock in the taskbar.
In theory if you were to uninstall Bit Defender Windows Defender will automatically turn on but this is not always the case but try it. Uninstall Bit Defender and any other anti virus software installed and see what happens.
If Windows Defender still does not enable you can try to enable via a registry hack. You can also do this through Group Policies since you Have Windows 10 Pro but the hack is quicker and easier. I have included a link below for you to download the hack. The hack does nothing but change a Group Policy setting.
http://jaylach.com/downloads/enable-defender.zipDecompress the file and then execute the .reg file. Make sure that you have uninstalled Bit Defender first. Let us know what happens.
Here is the content of the registry hack:
Code:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows Defender]
"DisableAntiSpyware"=-
Remember to only run ONE anti virus package. Do not try to run both Bit Defender and Windows Defender together.<edit>BTW, the above hack is proven in Windows 10 Pro only, not the Home edition. While I THINK that it will work in the Home edition I have no way to prove. The problem is that, unless things have changed, the Home version has no access to the Group Policies interface and the hack does nothing but change a Group Policy setting. Since the Home version actually DOES include Group Policies and the interface can even be enabled I would guess that it would work.