I feel Wizbones is exactly right in diagnosis. If that is the case, and you don't have the drivers, you should check the manufacturer's website, and then go to
Driver Guide using the username of "drivers" and the password "all". Uranium is right too, however, it can also be for other special controllers such as RAID.
The reason you can't install it on one computer and then move it to the other, keeping it just the same, is because of drivers being incompatible. you should change the drivers after you install it, and then instead of restarting, just move it then. That will work, but you should then re-install the drivers againt to make sure the registry has the right serial numbers and bus IDs for the components.