ok, more questions for ya then
is the ribbon cable that connects both sides together still in good shape? its not too uncommon that these break after all this time. check to make sure its not cracked in half or anything unusual
speaking of that cable... just for your general knowledge, don't plug it in and unplug the cable when the console is powered on. power it off before messing with that cable,
nothin immediately jumps out to suggest right now, i'll think of something in a bit,
but, it could also be the capacitors in the console. if they've never been changed (doubtful), they are past their life expectancy already. bad caps in the console being changed out have fixed all sorts of strange problems for me, including LCDs that behaved like this (seem to be OK, but no image on the screen at all). i'd suggest you give exchanging the caps a try. but, of course, that might not be the problem then you're out a cap kit...
i'm sure somebody else will have some things for you to try out as well. its pre-coffee/etc part of the day for me atm... my mind isn't quite up to speed yet