Well - I'd take that wireless card out and see if the lockups continue. Could be the entire problem right there. I had a graphics card in a SP 1.8GHz G5 that was a Mac
graphics card upgrade and supposed to work just fine and even after applying the fixes that were supposed to make everything all better, it still kernel panicked every time I woke it from sleep. Finally I just put the original graphics card back in and bye bye problems.
Can you look in the system logs to see if they reveal anything about the lockups? I'm assuming you're getting a hard freeze - not a kernel panic? Unfortunately hard freezes don't always yield much info in the system logs, though you should be able to see what processes were active just prior to the forced shutdown and whether or not it's the same event each time.
There are links to things to try here:
Freezing G5 Dual 1.8GHZ [Archive] - The macosxhints Forums
Note: coolant leaks are not applicable to your model. Nor is the random shut down caused by a faulty power supply.
Unfortunately, if none of the trouble-shooting in those links works, it's possible that you have a faulty logic board. That probably wouldn't be worth replacing in a Mac of that vintage, costing more than the thing is worth in total.
It's also possible that the hard drive has issues, though less likely. Still, if you can find another HD to try, that might be worth doing. (Do you happen to have Disk Warrior?)
Can you also run Disk Utility from the OS 10.4 install CD/DVD and see if there are any things that get repaired?