If you're making a portable you probably need something to watch it on. (Unless you want to guess what's happening in the game, but I wouldn't advise that) Anyway, this forum is your "Hacking a pocket TV/screen" one-stop solution. Share your experiences and knowledge here.
wall adapter usually supply about 2X the amps it takes so it probably takes no more than 700ma. you could either get 2 7.2v batteries with a regulator or 1 (if you console takes a lower voltage) and a step-up regulator
Stick an ammeter in the circuit whilst the screen is running and that will tell you how much mA the screen is actually using. As daguuy says, it's proberbly only using 700mA maximum. It will use even less if you do an LED coversion.
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yeah, totally look inside it for a regulator, you will probably find one. it may or may not have the part number "LM78xx" where xx is the voltage it outputs. give it like 3 more volts than that and you should be fine.