without trimming, the xbox can get down to about 9*9*1
...
but it IS designed like a computer, so it's going to be tough to find things you can toss out.
Battery pack wise, you would need a 12v battery with ~7 amps for every hour you want to run the thing.
For a reasonable battery life, you would probably want a 20 Ah pack
http://www.batteryspace.com/12-8v-lifep ... 200ah.aspx
http://www.batteryspace.com/14.4V-LiNiC ... Packs.aspx
4 of either of these could work:
http://www.batteryspace.com/polymerli-i ... roved.aspx for ~1.5 hours battery
http://www.batteryspace.com/polymerli-i ... roved.aspx for ~3 hours battery
Basically, you're looking at $200+ for a
smaller battery pack, and it'd still likely be larger than a DS just for the battery pack.
You CAN ditch the dvd drive, and EASILY, at that, and if you can afford to throw money at an IDE SSD, you can cut down on size and power consumption A LOT between the two.
http://www.google.com/products/catalog? ... NoBEPMCMAc
You need to be careful, as a lot of IDE "SSD"s on the market now, could be CompactFlash cards, and from what I hear, CF doesn't play well with the xbox.
A laptop configuration with no battery, and controller ports could likely be built for under $200 (and even in a single afternoon).
Sadly, though, to build anything actually portable, you could very easily, and very quickly end up spending $1000 or more on the project, and would have a Heck of a time selling it.