Leave your parts installed in the computer except for the hard drives.. Pull the hard drives and wrap them in aluminum foil, shiny side toward the drive. Then wrap them in bubble wrap. If you have a floppy drive installed, put a junk disk in it.
Assuming you have a tower case, ship the computer on its side, motherboard down. This will minimize the shock load of a heavy cooler on the motherboard. I do this even when I use a backing plate.