All of them are possible. Is an Intel motherboard also use? Details must be supplied. It's like finding a pin in a haystack if there are no additional info given.
As I recall there is an option in the BIOS on motherboards that I own that can turn off all but one core, and that is to allow "legacy" OS's to boot. I'm not sure what qualifies as a legacy BIOS, older than Win XP is my guess, since I have never had to use this option. I've never heard of turning off two out of four cores, but who knows what's out there. Otherwise, it sounds like a hardware limitation of some kind to me.