Power Mac G5 Quad: crashed and now seizing up and other major problems

Question

My Power Mac (G5 Quad) crashed twice today (screen froze and stopped responding to mouse and keyboard), both when rendering in an application called Artlantis, although that could be a coincidence. Another possible culprit is that I used Migration Assistant to move a user account, applications and root level files from an Intel machine, onto this machine recently.
After the second crash startup was slow and problematic. Mouse wouldn't respond although I was able to type in username and password to login. I was able to manipulate things with keyboard but not mouse. Everything seemed to seize up and then it would follow some of the commands I'd made via the keyboard and then seize up again. I do remember one other instance of having a similar crash and symptoms about a week ago, before I migrated the Intel-based account, so maybe that's not the problem.
I managed, with some difficulty, to start up with the Install disk (10.4.2) and do a disk verification, which brought up two instances of "Illegal name" (just after the word Catalog). I then did a disk repair which it said was successful. Restarted machine but same problems.
I've tried to backup some data that's not currently backed up, by booting into target mode but the machine tends to seize up after a while. All types of booting seems to be getting gradually more difficult. Leaving the machine off for while helps with booting.
Booted into super user and did fsck, which it said was okay. Booted into Hardware Test and did an extended test which said it passed. The Hardware Test and the super user mode seemed to be the only modes that could run without the machine seizing up.
To get the data that's not backed up off the machine I wondered about taking the hard drive out and putting it into another of our Quad G5s... good idea or bad?
As for finding out what's wrong, any advice?

Answer 1

Just some more observations. Hoping for new external hard drive to turn up today. In the time being I've been using the machine out of urgency.
The crashes seem to happen after an hour or two of using the machine. Most of the time there is no need for a hard shut down. The interface seizes up but after a minute or so I'm able to use the keyboard, including navigating between applications (command-tab) and shutdown (ctrl-eject -> tab to shutdown). Also, network or application processing activity continues, though what appears to be in a stuttering start-go manner. Activity on the keyboard seems to help this activity along, or at least helps you see any progress. If there's no activity on the keyboard the graphic interface catches up every moment or so on its own (just less often than if you're taping on the keyboard).