When you "reinstalled Ubuntu from CD", did you do this with the disk installed IN THE NEW COMPUTER? What I'm getting at is, whether the new computer is not recognizing the DISK, or it IS recognizing the disk but not the OPERATING SYSTEM installed on that disk.
Also, I'm not understanding the "unplugged the SATA connection and changed the BIOS" part. I am assuming you unplugged the SATA connection from the original disk, then plugged that same connection into the newly installed disk. If this is true, then why did you have to change the BIOS? Did I misunderstand the hard disk connection details? Did you change from a SATA to a PATA disk or something? I'm not understanding why you had to change the BIOS for anything.