PSOne Screen flickering/won't turn on with 9.6V NiCd battery

[gage]

I'm just trying to make a "no frills" portable NES. My original thought was to power the screen from the battery, then pull the +5v from the 7805 regulator on the back of the screen to power the NES board. From the sounds of it, this may be the wrong route to go...

That being said, would it be easier to power the NES board first (battery to 7805 regulator to NES), then run power from the NES to the screen? There's a way to step the voltage up to be used with the screen, right? I believe Ben's NES project from the book has the battery power going directly to the NES board first, then to the screen...

Thanks again for all of the suggestions!