If it's a 'branded' desktop computer why not remove the important components from it - hard disk, memory, processor, video card, optical drive - and then sell it as a bare-bones box on Yahoo Auctions Japan. If it's a 100% DIY machine then take the motherboard out too and pick up a new case back home for less than $50.
PM me if you want help with Yahoo Auctions.
Alternatively, since luggage allowances to the US are ridiculously generous, do your Asia backpacking on a return ticket from Japan and then fly back to the US from here. Leave your items here with a friend while you're away. So long as you travel back to the US before the end of the academic year ticket prices from Japan will be excellent.
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