Mac PPC G5 won't boot. Two beeps, fans, white LED blinks twice between pauses

My girlfriend's old G5 desktop was having problems, so she tried reinstalling (archive and install) Leopard from a DVD. Apparently it finished the installer, but would hang at the gray Apple screen.

I tried reinstalling Leopard and Tiger fresh, but both discs were kind of scratched and the installation wouldn't complete. Tried a retail copy of Tiger, but booting from the CD showed a gray screen with kernel panic text. Really great luck so far, right?

As as last ditch effort, I decided to try installing Ubuntu, knowing that a fresh DVD wouldn't have any physical problems that would get in the way. While booting to the DVD, the fans went on full blast and the screen went black for several minutes. The DVD eventually stopped making noise, and I gave up on that.

I thought there might be something wrong with the RAM, so I opened it up and took a look. The sticks were installed in two 256/512 pairs. It's not supposed to be like that, right? I removed them and reinstalled them in matching pairs and restarted. This time, the tower beeped twice (the second beep seemed slightly less loud than the first), the fans went on full speed, and the white LED started blinking twice, pausing, blinking twice, etc. I tried every conceivable configuration of RAM, including installing just one pair at a time, but the same thing each time. Powering on with no RAM resulted in a similar thing but one beep, so I think (hope) the controller is working fine.

So here's the question: is the RAM bad or did I screw up the logic board with my tinkering? How would I check to rule the logic board out?