Probably a good idea to NOT RUN THE MACHINE UNTIL THE FUZZ IS TAKEN CARE OF. Voltage has this way of accellerating electrochemistry.
On the 2000, you can get in there carefully if you have a good pair of wire snips (the pointy, shortnosed ones that are dished a bit for close cutting.. Just saw them at the local Dollar Tree, if that's any help) ... The 4000 looks like the same thing; you'll probably have to cut the single lead on one side, and bend it up a little to get to the joins on the other side.
http://amiga.org/gallery/photo.php?lid=116Drop the NiCd off at the local recycling center if you can, or plastic-bag it for household hazardous day; they're a bit toxic to chunk in landfill. (Or at least, do us a favor and wrap it in a few layers of Saran and a ZipLoc if you can't be stuffed the trouble; I don't mind cadmium in the ground as long as it's not leaching in my groundwater!)
Now as to the fuzz... I can never remember if ammonia (basic) or mild acid (vinegar) is supposed to be the right thing for this sort of corrosion. Brush and vacuum what you can manually, first, and if you use either, I'd suggest rinsing it cautiously, *cautiously* with clean water after the fact, so you won't have to worry if you've guessed right. (Just that one edge of the board, use distilled if you're paranoid, try not to get any in that yellow trimmer thing if your board is laid out like that one)... That said, if you've got the board out of the case, I *would* just pour from the bottle of distilled water over the section you've ammonia/vinegarized. Also be careful with your brushing and vacuuming - don't risk dislodging any of the surface mount components in the area. Just try to get off what you can.
After all that, my 'trick' would be to saturate that area of the board in WD-40. It's called "water displacer" for a reason; if you read the whole story behind the junk, it was initially developed to drive moisture out of connectors for the space program. Assuming the board is out of the case, tilt it up, and just go hog-wild with the spray can, whether the board is still wet from your other ministrations or not. Any water trapped under the chips, or for that matter, possibly any hydrous compounds formed by the corrosion, should be floated up and away. If it *is* wet, I'd come back in a few hours and shoot on some more, maybe once more after a day when you think things have dried.
*Then,* after some of the water displacer has evaporated (the stuff is rather volatile, actually, which is why it doesn't last very long on squeaky hinges or case fans; it's not meant to be a persisting lubricant)... maybe 24 hours or so... you can try to carefully brush whatever connector was hit by the corrosion, using more WD-40 if necessary, or some contact cleaner (should be available from Radio Shack, the UK equivalent of Radio Shack, or your local TV repair guy if you can't find it anywhere else).
Your machine will smell like WD-40 when it's warm for a while, but a week of running usually clears that up. Don't be too afraid if the exposed/corroded traces darken when you apply it; what happens is that the battery corrosion eats through the green/clearish mask they put on top of the PCB, creating porous spots - and attacking the traces - but if the machine still works, it works, and you can hope the penetration of the stuff will float up any remaining corrosives out of the metal. Again on the volatility front, don't be worried about permanently insulating any connectors with it, since it was designed for the task, and *will* evaporate eventually (if you can't get something to make good contact immediately after it's been cleaned)... I'd be leery of shooting too much directly into that trimmer, though. (Put a patch of tape over it, if you're worried about your aim. But I'm talking 'putting the little red stem on the can and blasting it right into the component might not be good.')
Do tell us which connector that was, though; it'll help us offer advice.
