well i went to gigabyte's website and used the model number you posted to look for a bios update and couldn't find one. so, either gigabyte no longer supports this product (so you probably can't use it with a duel core) or you have posted the wrong model number.
but, that model number did come up in google and i discovered that it will support pentuim 4 duel core cpus but not the extreme edition. this makes me think that it won't support a core2 based cpu either. so you could install a pentium 4 duel core... but i wouldn't reccomed it.
in the links you provide ,just to the right of the picture of the motherboard there is a related links box with a bunch of links in it about this board ,click on the one that says CPU support .if it says N/A in the right column,when you get there ,then it doesn't support that CPU .If it says f6/f7 then that indicates the bios version the board has to have to support the corresponding cpu . i check and in my opinion of the list neither one supports dual core cpu