What is the easiest way to move a Linux systems' discs a new computer, and get it to recognize the new hardware?
Install Linux on the other computer.
While a basic text/console based install can be moved to similar hardware (ix86 to ix86; IDE to IDE and so forth) any major changes are best delt with by a new install and transfer of needed files.
If you really think it's worth the work; shutting off start to Xwindows and working to add correct drivers or options may work.
Anything hardcoded into a setup text file can be changed with a Tom's floppy or Knoppix CD.