I feel your pain, G5 brother.
Lemme tell you what to try and do because I think I already know where this is leading.
If you've put any third party memory in, take it out, if you have lots of devices that are external detatch them. Start with a barebone system and try to make it crash. When it crashes again, you'll know it's at least the system itself.
You've eliminated those sources as things that aren't working correctly.
Next, you need to run all the hardware tests. Let it check the existing memory, let it check everything it can. If it comes up clean, don't pull your hair out.
I got my G5 back in oct, and it had system haults right out of the box. I knew it was the motherboard since day 1 and when they finally changed it out, that's when all the problems stopped.
You need to go through every possible option before you call apple, and then call them, explain what you've done and say, you need a either a service tech to come out or an appt at a store for further testing.
(Think of it this way, if your brand new computer is locking up all the time with an OS that isn't designed to lock up ever then you have to look towards hardware. Sure, there's a chance there is a bad install of the OS or some app that could be messing things, but again, the program should quit, rather than hault the system.)