Help with Raspberry Pi miniature arcade cabinet build (display/battery)

Hi everyone,

I've got a project going (well, in theory, I'm gathering a parts list) for a Raspberry Pi powered miniature arcade cabinet. To be up front, I'm pretty inexperienced with in-depth tinkering (I've done PC builds and some more surface-level and just-beneath-surface-level OS stuff). I have little to no experience with wiring and supplying power in unconventional ways (i.e. not a PSU), but that's kindof the point of this: I'm out to learn!

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via i.imgur.com (very rough mockup of my mini arcade)

I'm looking at using a netbook LCD (sourced from eBay) for the display, but that of course comes with some complications. The first matter was getting a controller, but it seems that kits like this have shown up around eBay as well, which include the controller and an inverter board.

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via img.auctiva.com

But there are two issues I'm having trouble getting worked out. The first is how to get the power to the panel/inverter. I'm planning on powering the whole cabinet with a rechargeable LiPo battery pack (micro USB out for the Raspberry Pi, not sure for the display). Does anyone have any clue how I would get power to the controller board and inverter? I seem to be at a loss here, and my googling skills aren't quite enough to figure it out.

The second, which is directly tied to the first, is exactly where that power will come from. I've looked into Lithium Polymer battery packs, but I'm not sure of the capacity I would need, nor am I sure if it's possible to charge it with a simple interface like a microUSB 5v charger, or if I'd have to use the big ol' chargers that RC cars and whatnot tend to use. Also, since the same battery pack would be powering the display and the Pi (the Pi via micro USB, the display via... ???), do I need to split the output so it's going to two sources, or would I just funnel it all through the Pi (seems that would be too much power to go through there)?

After these two issues, everything else should be a breeze (setting up the Pi for MAME and other emulators, building the joystick/pushbutton setup, etc.).

Thanks for any help! And of course, once this gets off the ground, I'll be sure to post some build shots and the final results in here as my display of gratitude.