You can't swap hard drives between computers like that in general. In some cases it might work with errors, but the main CHIPSET on the motherboard probably needs to be identical at least.
You would also have to change the BOOT ORDER so the new drive comes first or simply UNHOOK every other hard drive (rear cables) then try to boot.
In most cases:
You would have to REINSTALL the program to the new computer, then you could add the old drive as a backup disc and search for any files that you may need.