Thanks for the tips, equill. I removed most of the chemical goodness with soapy water, though a fair amount remains on what's left of the one machine. I kept the parts of that one because externally they're in fantastic shape. If I ever need to use them to restore a busted machine, I'll put more effort into it.
Anyway, update time.
One of the machines had a leaked battery. I initially thought it was both due to another condition of one of them, but that was not the case.
So I took the leaked battery one apart first. Immediately, I notice the extent of the leak. It mostly affected the top and bottom case plastics and the trackpad so far as I can tell. The trackpad clicker button and the sleep switch are toast, and there's noticeable corrosion on the trackpad cable. So that's scrap. The clicker and the rest of the trackpad support are broken, so they were gone. The top case had a crack on one side, so it got tossed, as well. The motherboard had one of its battery contact sets completely corroded off. There were spots of corrosion elsewhere on the board in the battery power area.
On the plus side, the display is in fine shape (except for the missing clutch cover) with a good screen. The keyboard is in great shape with minimal wear. The centre support is good with minimal corrosion that was easy to remove. The drives were unaffected by the leaked battery, and currently work flawlessly. Also, there was a 32MB RAM expansion card in this one (score!). While this one was soaking, I started in on the other one.
As you'll see from the pictures, the display on this one was destroyed in some way that I couldn't explain given the condition of the rest of the computer. Anyway, I took it apart, and there is corrosion all over the centre support. Happily, the drives and everything else were not affected by it, so I just tossed the support frame out and substituted the one from the other machine. The plastics are in fine shape, so I reassembled the bottom with its new innards, swapped the display over from the other one, and everything was golden. The machine powered up and loaded KanjiTalk 7.5, which I promptly replaced with an English version of System 7.6 (because I don't know Kanji for crap, and don't have any Japanese apps anyway). This machine also had a good hard drive and floppy drive, so the ones from the other machine are being kept for spares. Installed in this one was only the factory 8MB memory module, so I swapped over the 32MB card from the other machine.
The packaging for both is in great shape for being 13-year-old cardboard and styrofoam.
So that's pretty much the end of this story. The currently working model has the 25MHz 'LC040 with 36MB RAM, 240MB HD, one dead battery and a battery blank. Plus I have a new cache of spares, including an extra set of screws.
Finally, the pix:
http://www.flickr.com/photos/15550281@N03/?saved=1
That takes you go my Flickr's home. I really have nothing besides several of these computer pix there right now, so have fun.