Ran Apple Hardware Test from original Tiger install disc to diagnose recurrent worsening inconsistent kernel panics. The Hardware Test hangs up at 35 seconds, while "testing memory." The first time I ran it I didn't realize it had hung up till I looked over the display after 3 or 4 minutes. It showed "Detected Error" and a code, but shut down as I scrambled for a pencil to write it down. I then ran it 3 more times, but each time the system shut down sometime between 35 seconds and the appearance of the error code. Can I deduce anything useful from this? Can I force the Hardware Test to tell me anything more?
I'm not sure if there's a way to get more information out of the Hardware Test (although I would suggest taking a picture of the screen if you're not able to write all the info down in time). However the symptoms you describe suggest that there's a problem with your memory — either the sticks themselves, or the memory controller.
I would suggest taking out your memory, then trying these steps:
If you find that one stick works but the other doesn't, it's likely that you have a bad stick — replacing it should solve your problem. Likewise if new RAM works but the existing doesn't.
If you find that one slot works but the other doesn't, then you likely have a logic board or memory controller issue.
Finally, if none of those combinations work, it could be a logic board or memory controller issue, or something else.
Sorry I can't be more definitive, but hopefully that will help you to narrow it down.
The AHT result codes and triage steps are not published to Apple except to trained / authorized technicians, so the obvious thing to do would be to call one and ask for a quote.
They may want you to relay the results or they may prefer to run the tests themselves since it might take more time to pore over your results / check your work than to do an estimate by their trained techs.
When the system can't even complete a hardware test without powering off, it's most likely not the memory since you could pull all RAM and repeat the test with only one memory in one slot and perhaps try a second memory in another slot in case you feared one receptacle or one chipset was horribly damaged and bringing the entire Mac down.