yeah, i agree with Ashen's point, the cube needs a battery life of about 12v and a 7.4v won't cut it,
with a small battery than 12v, maybe 11v, the cube won't have the power it needs to run for a longer period of time
the cube originally runs on a 12v power supply with it's regulator spiltting the various volts into the require areas needed for the cube to work with.
the "best" kind of battery pack is a 14.8v the mah is up to you really, but must be more than 4500.
I'm going to use a Li ion 14.8v 6600mah pack x 1 (on amazon, the battery info specs say not to wire this kind of pack in Parallel as it scan be very dangerous and is not recommend.) Both li ions/Lipos really.
but, if you use a volt battery higher than 7.5v for the prone screen, you must regulate it down to 7.5v for the screen to get the exact amount of power it needs to run without it ever frying, a step down adjustable regulator works well for this since you can turn the little screw switch of the box and change the voltage you want to the desired output.
anyways, you mentioned about the screen and gamecube not running at the same time and only one at a time. um, i read console modding site:http://kyorune.com/modding/article.php?id=17
about for the console and screen to work, i found a helpful hint, i think this may help you:
"If you're using different power sources for the screen and the console/whatever, make sure to connect the grounds of the two together!"
also, i messed up my Disk cover lid etc, so i had to use my prone cover case. i really liked your idea of the psone cover as a disk lid for the gc dd. so I'm using your method too
. a much better way to make a discover for the gc DD than it's default one.