First, the obvious. Are you pressing the button for too long or too short? DO the fans spin when the button goes on and off? Do your APCs have a “warm up” time? It sounds like maybe they aren’t completely powered up when you try and turn on the G5. If you totally unplug a G5 from the wall and try and turn it on, the little light will still come one in the front for a bit and then go off. There’s some power stored in the power supply somewhere even though it’s not receiving power from the wall.
When you say power supplies, you mean some sort of battery backup APC, and how old is your G5? I found that this will drain the little internal clock battery (also called a PRAM battery) faster than when the unit is plugged into to constant power (with the G5 turned off). You might want to try replacing that battery. I forget the size of it, but it’s something like a 3.6v lithium. OPen your G5 and you should see a little half size battery attached to the mother/logic board. You can pull it out and check the requirements/size. Any Radio Shack should have it.
Jeremy