Would help to know your Mobo + rev and your BIOS version.
The 965 is a four core chip fab; it would never have been locked out at the factory, so BIOS based core unlocking/UCC/etc. shouldn't be necessary at all. The only way I could see it being made unavailable by BIOS settings would be specifically disabling it under [active] core control, so that would be the first setting to check.
The next step I would probably take would be to flash the BIOS with the most recent version available. I've seen cases where the BIOS didn't have specific support for newer chips on the same socket type and that caused the same kind of problem. That kind of thing is generally a pretty big deal, so you should expect it to have been patched out by now.
I should ask for the sake of thoroughness, how many cores Windows, CPU-Z and OHM are all seeing.
And yes, more physical cores is [hypothetically] always better. Even if your game(s) don't make specific use of more than 3 threads, Windows scheduler still decides which core to run each thread on. Being that Windows will always have overhead and probably plenty of discreet processes, it's beneficial for OS agility to have plenty of free cycles lying around on an unused core or two.
