Right, I am using Win 7 (w/sp1) 64bit. I had thought I was using the most recent AMD Sata controller driver as I went to the motherboard's specific support page for downloads, and got the most current one there. But your response did prompt me to look into the driver more closely. Thank you.
I had been using an old driver. With a newer driver, the issue is solved, and the full 4TB drive is now seen.
The version of the AMD SATA driver that does not see it is dated 05/05/2009 with version 1.2.0.125. (That's the one you currently get if you download from the MA785GMT page on USA site.)
But, on the general downloads section of the gigabyte website, NOT on the support page specific to the MA785GMT motherboard, there is a newer driver dated 10/12/2012, version 1.21.337.
After updating to this newer driver, all is well.