Basically, same issue as described in this thread:
BD Total Security installation doesn't start at all — The Bitdefender Expert Community
My machine had an issue, just after some initial installations, that I needed to resort to a Windows Restore Point. My assumption is that it went back before BitDefender was installed, but still leaving some of its files loose around.
Anyways, the symptoms:
- I start a new installation, it passes the first checks;
 - It asks me to reboot the machine so it will continue afterwards;
 - I notice that a new folder is created in c:\Program Files\BitDefender\{Random Guid}, but no file is placed there
 - After reboot, nothing happens
 
I've already done:
- Booted in safe mode;
- Excluded all folders named BitDefender in Program Files (both x64 and x86), ProgramData, %temp%, AppData\Local (traversed thru all users folders).
 - Excluded all registry entries named "BitDefender"
 
 - Cleaned all BitDefender related autorun entries and remaining services (using SysInternals Autoruns)
 - Disabled Windows Defender Real Time thru ordinary UI and thru group policy (gpedit.msc)
 - Tried to install both using both the offline and online/on-demand downloader installers
 - Tried to use the BitDefender Uninstaller Tool provided in this link
 
Obviously, I don't want to fully format my PC. I don't consider it as a viable solution for me now.