FINALLY, I got 8.1 to install! The only thing different was I checked today and there was a Windows Update marked "important" and just 2 days ago. I was upgrading a Windows 8 Pro 64bit OS to 8.1 Pro 64 bit and had ALL updates posted until today. Even though it's dated as 2 days ago, I think it was post very recently.
I double checked my BIOS, graphics card drivers, etc. and all were up to date from the manufactures web sites. After installing this new update, I decided to try to install 8.1 again from the MS Store. Everything went as before, but this time it got to the "Setting Up" stage and kept going with no problems at all. All I had to do was log back into my MS account with the same info I used in 8.0 and everything was there. The settings, programs, etc. were ALL just fine and I now had a fully working 8.1 version.
It's unknown what this update may have done, but I know it was NOT there a few days ago. For those going through a lot of trouble, I can relate, but it's almost never all the stuff they are saying like uninstalling anti-virus, unplugging devices, etc. Everything on my PC remained exactly the same, I did NOT remove a single program or driver and kept all USB and other devices plugged in. It just simply worked this time with no problem and must had to do with that one new update.
Good luck to others, I'm sure you will get it going to, just a matter of time for updates to drivers and MS patches like the one I tried. Hope things go well.