If you really need the computer, I would not EVER airline it. (I use to work as an airline pilot, until I switched to business jets.) You would be surprised the amount of items stolen, much less broken during transport. The airlines specifically exclude any reimbursement for electronics of any kind in checked luggage, and it is probably too big to be carried on.
What I would do is ship the computer to your business/hotel/etc. instead, using a shipper with insurance, such as UPS/FedEx, or the USPS. Make a shipping company responsible for any loss or damage, rather than checking it as luggage and accepting the loss yourself.
Good luck.
Absolutely the best advice. As a very regular air traveler, I would never consider either trying to carry something like that on and definitely wouldn't check it.
I just googled 'luggage limit of liability' and hit this (not to pick on AA, but I'm sure it's similar on all airlines)...
http://www.aa.com/i18n/customerService/customerCommitment/conditionsOfCarriage.jsp#Baggage
American assumes no responsibility for loss, damage or delayed delivery of transferred baggage not acceptable for transportation by American as checked baggage, items damaged as a result of items contained in checked or transferred baggage, and items accepted by American pursuant to the execution of a release form. American does not accept in or as checked baggage any of the following items: antiques, artifacts, artwork, books and documents, china,
computers and other electronic equipment, computer software, fragile items (including child/infant restraint devices such as strollers and car seats), eyeglasses, prescription sunglasses, non-prescription sunglasses and all other eyewear and eye/vision devices whether lenses are glass, plastic, or some other material, furs, heirlooms, items carried in the passenger compartment of the aircraft, liquids, medicines, money, orthotics, surgical supports, perishable items, photographic, video and optical equipment, precious metals, stones or jewelry, securities and negotiable papers, silverware, samples, unique or irreplaceable items or any other similar valuable items. American does not accept these items in or as checked baggage and assumes no responsibility or liability for such items, regardless of whether American knew or should have known of the presence of such items in checked or transferred baggage. If any such items are lost, damaged or delayed, you will not be entitled to any reimbursement under American's standard baggage liability, or under any declared excess valuation. Do not attempt to check these items. Carry them with you in the passenger cabin (subject to carryon baggage limitations).