Well, I got the worst of the muck off and... well, it's bad, but not as bad as I expected:
The attachment Toshiba_110CT_UnderTheMuck.jpg is no longer available
Slightly disappointed. I was half hoping for a nice clear 'this is broken and fixing will take more time than I really want to spend' amount of damage, rather than a 'well, maybe' amount.
There are some broken traces, but all the pins on the 187HP look intact, if a bit thin. Elsewhere, near the second battery plug point, I can see a couple of traces that may be broken, but this area is the worst of it. I think the next step is to see if I can get the 187HP off without breaking any pins. I suspect that the gunk will have glued the pins to the pads and made the metal brittle, so removing it without doing damage could be fun. Then the keyboard connector, which I'd like to try and save if possible but can be replaced. Then those 62Z components (dual diodes I think, HZM6.2Z) and some of the resistor packs. Also want to try and remove the rest of the CPU heatsink to see if there's any more damage.
I think the odds of it working might have doubled. Up from nearly .0000001% to nearly .0000002%.