Thanks, I hope I'll manage to google it somehow...

I'll clarify: 3.4-3.5v

Im almost positive the output of the DMG's power board is 5V (see that pun there ) so 5v is the highest

Dude, Nitro is hella cool. Visit his website... you'll learn things.

It was intended to be a wild exaggeration (I know you can't boost voltage x2) and I think 3.4-5v is about as low as you can get...
Anyway, running 9v strait into the DMG is a colossal waste of power, as the regulator will just convert any extra power into heat, and I'm not sure the regulator in the gameboy can handle 9v for an extended period of time. My idea simply extends battery life and eliminates the risk of damaging your DMG.

Just letting you know, you should know that yes a dmg will run from a 9v battery, it is the battery life that should be your concern.

Talking alkeline batteries, here is the comparison of mili-Amp hours (mAh):

AA: 1800-2600 mAh
9v: 565 mAh

As you can see the juice in a standard alkeline AA is 3.18-4.6 times more.

Talking lithium batteries:

AA: 2700-3400 mAh
9v: 1200 mAh

As you can see the juice in a standard lithium AA is 2.25-2.83 times more.

You can read up about them here:

http://en.wikipedia.org/wiki/AA_battery
http://en.wikipedia.org/wiki/Nine-volt_battery

I would also recommend looking here:

http://en.wikipedia.org/wiki/Linear_regulator

However,

Well, from your reply I wasn't sure if you understood my post, so that's why I pointed out the regulator/converter thing. Since you mentioned 2.3 V, even if a made up number, I assumed that what you were addressing was the problem of the voltage being too low when the batteries are about to run out.
With regard to the LCD, the first thing to do is to establish whether the LCD is at risk at all. If not, you can just use a 9 V battery and be done with it.

Yeah right, I think nitro should just shut up. You can build it smaller anyway.

2.3v was just an example, and I haven't tested it. It was simple nonsense, and your semantics aren't necessary.

That's what I'm saying, though. The DMG already has such a converter (even if I called it regulator). When the voltage of four AA batteries, or one 9 V battery is 2.3 V, no boost converter in the world will save you, because the battery's internal resistance will stop you from getting enough current to power the Gameboy. In my test, the Gameboy used 120 mA at 2 V. Trying to do that with almost fully decharged batteries would probably be impossible.

I can build a smaller one.

That's what the buck boost converter would be for. No matter what the battery voltage, the output will always be 6v. Battery down to 2.3v? Output will stil be 6v. So you'll have power right up until you don't...

A voltage regulator is just a self-adjusting "resistor" (also known as a transistor, you might have heard of those) that does the same thing as described in the calculation, but over a big voltage range. From about the output + 1 V up to when the regulator circuitry breaks down. The downside of either the resistor method or the regulator method is that energy will be wasted as heat to warm up that component. The downside of sing the resistor method in particular is that the voltage seen by the Gameboy will go down as the battery's voltage goes down, which makes  the Gameboy use more current to maintain the same power. You might also get a change in LCD contrast when LSDj plays versus when it doesn't, as it enters a power save mode when it's not currently playing.

Thing is, the Gameboy has a so called switching voltage regulator which can handle a wide voltage range, from at least 4 V up to maybe 9 V or more. The voltage regulator is of the switching variety, which means it regulates the voltage level by turning the input voltage on and off at a high frequency. The DMG regulator also has a transformer which allows it to both boost and "buck" (lower) the voltage.

The potential problem, apart from going outside the range that the components in the regulator can handle, is that the LCD supply voltage will vary with the battery voltage. The increased voltage with increase LCD voltage could (Not will. Read exactly what I said.) destroy the LCD on the extreme contrast setting. This remains to be seen, however and it should always be safe for the LCD as long as the dial is set to a normal, legible setting.

also: this is the smallest buck converter I found on ebay (20 x 20 x 5mm)

SICK! This (at 6v) is what I need for my keyboard!

Not exactly the same, but:

Gameboy pocket with mini usb (for charging only). It has a li-po battery similar to this one (600mAh) and this lipo charger (cut down in half). You can also get the charger at sparkfun.
I have yet to put the battery life in a serious test but it seem really good (at least compared to the crappy AAAs I've been using before). I can also use my USB EMS with no problems.

I have it dialed down to 5.8v running it through some resistors and a converter on a breadboard right now.
Gonna see how everything goes, then I'm gonna experiment with a LTC3789 buck boost converter. That should be significantly more efficient, and have comparable battery life to the 4 AA's.