OK, I'm back.
Specifically, I'm back because I solved the issue and now have 64-bit Win 7 running with 8 GB of RAM.
I've solved the problem where my Gigabyte GA-MA790X-UD4P would BSOD (blue screen) during install of 64-bit Windows 7 with a message about the BIOS not being fully ACPI compliant if there was 4GB or more of memory installed. Also, it would not boot with 4GB or more memory.
You're asking yourself, "Self, why did he put that in the message? It's all in the thread above." Well, self, the idea is that after the search engines crawl this forum, someone else with a similar problem who does a search with Google, Yahoo, etc. will hopefully get this message high in their results.
Anyhow, here's what fixed it...
Sometimes, you can be a bit too clever. I was trying to minimize things as much as possible to try to prevent issues. I had various system peripherals and such turned off or disconnected to try and minimize the system as much as possible. The MoBo has eight SATA ports on it. Six are provided by the AMD chipset and two from an onboard "Gigabyte" (JMicron) chip. Either can be configured for "fake RAID" (software-based RAID). So I decided to connect my two hard drives to the two "Gigabyte" SATA ports and configure them as a RAID 1 array.
The rest of the internal devices (DVD-RW drive, an old Zip drive) are holdovers from my last system and use an ATAPI interface. So when I set up the MoBo in the BIOS, I realized that I needed the "Gigabyte" SATA ports, but not the AMD ones since I had nothing connected to any of them. In the BIOS, I disabled the AMD SATA ports since they're just sitting there empty. Less is more, I thought. The more I simplify the system and get rid of stuff I wasn't using, the less likely it was that there would be problems.
Today, I went through the BIOS settings, just "trying things" to see if I could make a difference. Finally, I tried enabling the AMD SATA ports, that are still just sitting there, empty. Ta da! The system booted without a hitch. When I got into Win 7, of course, it detected the new device and wanted drivers. I installed AMD Win 7 drivers I already had on a floppy and everything seemed fine with 4 GB in the system. I tinkered around to confirm that it was the, "enable the AMD SATA ports," setting that was definitely the one that made the difference and once I was sure, I popped in the other two modules to bring the system up to 8GB, and it ran just fine.
I'm going to wring it out over the weekend to be sure, but it looks like that solved the problem. I haven't tried a complete reinstallation to see if it solves the BSOD during install, but it certainly fixed booting with 4GB or more. And, even if it still won't install with 4GB or more, that's no big deal. I'll just pull three modules, install Win 7 and then put them back. However, I suspect that it's probably solved that problem as well since previously I could also get the same BSOD if I asked for a "repair" during boot after a failed boot. Now, that's gone, too.
So, all I can say is it fixed the issue with my specific Gigabyte board. YMMV.
Thanks to those of you who offered ideas over the last week or so! If someone else pops up here with a similar problem, you've got some new information that might help them.