Hey there, SwankyDanky.
So from what I understand the computer works normally when you have just the old drive connected to the motherboard, is that correct? If "yes", I'd suggest that you try the new HDD with a different SATA port and SATA cables, to see if the same thing happens. When you have it connected along with the old drive, go to your BIOS and make sure that the old drive is the first booting option in the boot priority menu, to see if you'd able to boot to Windows properly this way.
If you are able to boot to Windows, reformat the new drive and try the cloning process again. You could give it a go with different cloning software, just to see if the same thing happens. Other than that you could download its manufacturer's diagnostic tool and test the drive for errors, to see if there's anything out of the ordinary.
Hope that helps. Please let me know how it goes.
Boogieman_WD