Referring to bassfisher, I can see all my eight cores of AMD FX 8120 processor in Device Manager.
It's possible to lock cores in BIOS, but then you should see the options there. And, at least with AMD, there are software that can be used to lock / unlock cores from within Windows. Don't know Intel, but probably they have that kind too, although it seems unlikely that you have this kind of software installed, since the OS has only been running a few days. That could depend on what sort of installation you made. If you merely updated, there could be residues.
You could solve the issue with a BIOS update, perhaps? CPU running at 100% isn't that worrying, since electrical equipment are built to do that - if it runs at full power all the time, it's probably a malfunction or some nasty program taking all power, even some respected Antivirus programs do this, or it could be an infection.
Like you write, it's quite possible that one of the cores can't run = is broken. It happens, nothing lasts forever.
Hope you get it running.