Hey cool - thanks for all your responses! Where to start? Yes, it's always the same or pretty close - 8-10 minutes to freezeup. I agree with the guy who said don't do this too much, and I don't leave it on after it freezes.
I have pretty much eliminated disk problems, since it exhibits the same behavior with the 160GB drive, the original 30GB drive, and when I boot up the install cd/dvds, both Panther and Tiger. The problem will show up on time, even if the machine is idle - doesn't seem to be tied to disk access.
I got a utility called iStat Nano, runs on the dashboard and tracks temps in several places - CPU, HDD, GPU, a couple others - I haven't seen anything over 34 degrees before the freeze. When the computer was working, it would get much warmer than it gets now. I have also run the iBook with the covers off, and felt around the logic board and there are no hot spots apparent. Of course, the heat sink gets warm. I think I hear the fan briefly run during POST, haven't heard it otherwise. And no system or error log entries about bad hardware. I've sent off to Apple for $23 worth of AHT disk, don't know that it will point to anything, but I'll try it.
Back to the heat sink - I lifted it, and found these sticky pads between the chips and the sink. Are evidently some kind of thermal transfer material, packaged so you don't get your fingers dirty (Macs! I've never seen these in any other technology.) I removed the pads and applied paste to the chips, but I found that without the thicker pads in place, the GPU and the big chip in the middle don't quite touch the heat sink. So I reapplied the pads to those, and left the paste on the CPU. Do those pads ever need to be replaced?
In the olden days, we had something called thermal runaway - a resistor or capacitor would fail, allow excessive current to flow into a component, heat it up, leading to more current flow, and so on until the major component failed. It sounds very much like what's going on here, but then, we weren't dealing with components the size of subatomic particles. You could usually see the bad piece blistering the varnish on the PCB. How do you find it now?
What else? I have run this with and without the AC plugged in, no difference. I suspected that something might be pulling a voltage down somewhere, but if it isn't the DC-in board, it's big trouble.
So thanks again for your help. I'd really like to fix this iBook, it's for my daughter. I'm hoping to keep it going until she goes off to college and gets a brand new MB. By the way, I'm writing this on my 13" MacBook, my other daughter has a 15" MBP, and among the family we have an iPhone, two Touches and an iPod Classic. So our Apple dues are paid up!