I'd like to power a small, headless, linux box in the desert for 10+ hours a day. It draws the lower end of 30-40 watts. I'd like to not use a generator and go the battery + solar route. Can you tell me the best setup I should use in terms of battery size vs solar panel output?

EDIT: Adding additional info:
The desert where this unit will be for a week will have about 5 hours of useable sunlight each day (Black Rock Desert, early September). The computer is a standard shuttle (mini-pc) with SSD and wifi (more details in the comments). I know I can get lower than 30-watts PC but for the application and user load I expect, I'd like to stick with what I have now for the initial version (though hardware suggestions are always welcome).

I will be charging the battery up fully before the week long stay, which would allot me a little time with no sun / solar panel setup. Thanks.

**Update!** I took some advice below and got an old NSLU2 off of Craigslist for $45. Now I'm running a Debian web server at 2.5 watts! (6.4 watts with two usb hard drives and while transferring files.) I may be able to run the whole setup off a battery all week without the need for a charge.