So, for anyone with a Pentium D chip, just FYI, we were still having problems with the 32-bit install of 7. I finally started taking some other things out of the equation, such as the new RAM I bought for the upgrade as well as the video card. I changed out the new RAM for the old RAM she had in there and 32-bit ran without any issues. Obviously there was an issue with one of the simms.
Knowing that I couldn't run the 64-bit with only 1GB of RAM (what she had in old RAM), I went out and bought two new 2GB simms and put them in and reloaded 64-bit (build 7229 - which is what I have on my machine). It's been running now for a day and a half with no issues.
So, bottom line, Pentium D CAN run 64-bit. All along this was a RAM...