Bring it on the plane, excess baggage. This way you can keep an eye on the box and avoid the baggage handlers. I am wondering about getting the box through security without the hassle of opening it over and over again. Ask about having the box sealed with security tape and/or better yet, sealing the box in a heavy duty, clear plastic bag, taped closed by security.
Placing the boxed computer in the baggage area is asking for trouble. Crack the screen and you can toss the unit in the trash.
Make a back-up of the hard drive before boxing it away for your flight. Hard drives can be damaged at anytime. Better safe than sorry.
Let us know how it all went. Others will learn from your experience.
SK