All you need to do is deactivate (check mark remove serial number) and uninstall if you are going to give the computer away.
computer. I have the original disc so I guess I'll have to transfer it
out of the old computer.
That doesn't make sense, if you have the original install disc, you need not and should not transfer anything. You insert the disc in your new computer and run the install.
If you mean to tell me you do not have the install disc, then click on the link for a trial CS4 installer, download it to your new PC, enter the serial number and activate.
Gene