jdcranke07 :
it has nothing to do with the GPU/video card. It is something to do with your motherboard/CPU/RAM combo. Everything I'm reading is saying that your system is perfectly fine for running windows 10. What I have read though is saying that your system will show its age regardless if it is capable or not of running Windows 10 because your computer was not optimized to run it. But, you meet the RAM requirements, your CPU is capable of running x64 architecture, and you have adequate HDD space. To me that sounds like you might need a BIOS or driver updates in order to run the new OS.
---------------
Thanks jdcranke07,
(I hope this is a response to your answer instead of posting a new solution as it definitely is not a solution)
I'm running the last BIOS update that was available. I have over 500GBs available and I'm running Windows 7 64Bit now. I have run Microsoft's software to verify I can run Windows 10 and it passes. But after upgrading to Windows 10 things like the Start button, Cortana, Edge, and Search (and some others I can't remember) do not work. So I put my cloned drive back in and resume running Windows 7.
I really don't want to give up this computer as it is one a very few PCs that has hot swap hard drive bays up front. I used those all the time to do my weekly backups. I don't really do backups in the normal way. I do clones every week and rotate between 4 hard drives. But it looks like I'll have to start looking for another PC with that kind of capability.