IF they are identical in every respect as you've indicated and they are or at least both were running the same previous version of Windows, then.....
The problem may have something to do with this.
http://windows.microsoft.com/en-US/windows-8/what-is-pae-nx-sse2
As the information in that article suggests, checked the BIOS and make sure that it is enabled on the problem machine. I'm relatively certain that the processor supports 10 if the BIOS is configured properly.
Maybe even compare the BIOS configuration between the two machines and confirm that the exact same settings are available on both.
There may even be a BIOS Update required that may have been performed on one and not the other.