So I've installed Microsoft Visual C++ 2010, and shortly after that I've also downloaded and installed Security Update for it. As for DirectX, my computer already has the newest version of it installed - it says.
After all that, I've tried installing AMD CCC 12.6 once again (this time drivers only, minus the CCC itself, as DigDeep suggested). After restart, and "Starting Windows" screen -- same problem appeared...
Black screen, few seconds later desktop showed up with no icons/taskbar/mouse cursor. After doing Ctrl+Alt+Del, the black screen (previously mentioned) showed up once more, and from there on I had to manually restart PC; boot Windows in safe mode and restore system to a point prior to AMD drivers installation.
Long story short - the issue still exists, I still can't start up Windows normally after I install AMD Drivers. Also, MSI Afterburner 2.1.0 setup shows up every time Windows loads in now, asks me if I want to install it :/. Sigh
Thank you, Solarstarshines and DigDeep. I appreciate your help! Still looking for suggestions..