Finally, things have progressed from bang-head-on-wall to ... well, progress.
First of all, I've solved PART of the issues with the Mayhem G3 laptop. I'd previously checked the fans and heatsinks, and they looked fine ... from the outside. Yesterday, at the suggestion of a friend, I partially disassembled the laptop in order to replace the heatsink themal compound. (A good call; what was there was mostly gone. It's now been replaced with a fresh layer of Arctic Alumina.) And, so long as I had the heatsink assembly out anyway, I disassembled it for a thorough cleaning.
The Mayhem's CPU heatsink is basically a fan-pressurized plenum assembly with fine copper-fin heat exchangers at either end, connected via heat pipes to the CPU. The inside surfaces of both heat exchangers were totally blocked by a layer of dust so thick and dense that it had formed what amounted to a 1/8" layer of solid felt. NO WONDER the previous owner had reported that it had begun "crashing" at increasingly-short random intervals; it had no cooling airflow whatsoever, and was going into emergency thermal shutdown to avoid destroying its CPU.
With its heat exchanger cleaned and new thermal compound, the Mayhem is now stable running Windows XP Pro, and has been up for two days without a hiccup; I even stress-tested it playing Halo for about twenty minutes, which was driving it into thermal shutdown within about two minutes prior to the cleanup. (I will note, however: If you value your sanity, don't ever try to play Halo — or probably any FPS — with a trackpad. Just don't.). So, one problem licked; I know the hardware is sound. Next, I get to re-tackle the problem of getting it to boot under Linux with ACPI enabled. (Which may now be a solved problem — it is entirely possible that what was happening was it was getting as far as loading the ACPI code, detecting thermal overtemperature condition, and immediately halting.) With a 100GB hard disk (well... about 94 real GB), I have it partitioned 45GB and 45GB with a roughly 4GB swap partition, and I'll be leaving the XP installation in place and installing Gentoo dual-boot.
Given this success, I went on to also disassemble the M5309 laptop, which I'd been trying to reinstall for the Dread Pirate Bignum (who has decided to name it Post-Dated Check Loan) until it became unable to successfully compile anything, and replace its heatsink thermal compound as well. (Which turned out to also be a good call; it was that horrible grey waxy stuff, and very little of it was still between the heatsink and the die.) I then set out to try a new clean install, which not only exhibited no further problems with failed compilations, but successfully recompiled gcc on the very first try — always a good stresstest of a system. But it still wouldn't build glibc.
And this was where things REALLY got interesting.
( Beware; here be deep geekery. )
Now, with that all figured out, Post-Dated Check Loan is happily compiling away, installing a complete clean system from scratch. So Pirate is going to have her laptop after all in another day or two. (We should probably buy her a new battery at some point though; the one we got with the laptop is down to 29% of its original 4400mWh capacity.)
Then, assuming I can sort out the processor speed control issue on the Mayhem laptop, I just need to source a screen from it somewhere. (It requires a Quanta QD15LT01 15.4" WXGA active-matrix TFT LCD. I can find one for about $60 used and asserted to be in good condition, about $77 for a "100% compatible" knockoff with a high-glare gloss surface, or $95 for the genuine article. Saving $18 for a knockoff screen that I already know will have a glare problem just doesn't seem like a good idea. But whichever I buy, it's going to have to wait on budget.)