The G5s are definitely finicky when it comes to "Staying alive"... Many water cooled versions leaked and basically ruined the power supplies (located on the Bottom) and often the system board also. The "air-cooled" have better luck, but also have a habit of developing a "Sudden Death Syndrome" sometimes you can take one apart, re-seat everything, and bam, back to life, other times you will change the PS and still no good, or a Logic board swap and you will still be scratching your head wondering WTF is wrong. RAM must go in pairs of equal size and from the middle out, and other ridiculous crap that makes you wonder what Apple was thinking.
Repair guides attached, I have be fixing them since the first model and they all suck.