Switch cleaner has worked and the machine is now happily running again!
The list of faults is pretty trivial now -
1) Caps Lock LED doesn't seem to work (this was always faulty before, I think its the LED itself rather than the connections to it).
2) One rubber foot unstuck at the back, and both of them look too small to be the original items.
I can live with those!
So in summary, if your battery leaks, these are the things that could go wrong:
a) CMOS RAM chip. These are a PCF8583, and are available on Ebay. If you renew one, it might be a good idea to socket the replacement.
b) Keyboard - either due to broken PCB tracks, failure of IC4, IC5 or IC10, or gunk affecting SK7. All the ICs are available and replaceable, but I have not found a direct replacement for SK7. Note that some forms of damage will prevent the POST error code from flashing the floppy disc light (because this signal goes through SK7).
c) Mouse - damage to PCB tracks, zero-ohm resistors or socket. Resistors can be replaced with wire links and apparently-compatible replacement sockets are available from Farnell, though nobody has tried them out yet!
d) ROMS - check especially the pins nearest the battery. Pin 1 on each rom should be connected to pin 1 on the other three, etc. If the rom connections are damaged the machine will not boot at all and you won't see a POST error sequence.
Pretty much all of the above is fixable with access to the circuit diagram, a multimeter, a sharp soldering iron, side cutters and Kynar wire. So don't despair!
As a result of fixing "machine 1" I no longer have a lot of enthusiasm for fixing "machine 2" that I bought in a moment of weakness as a donor (and which I described repairing earlier). This machine is cosmetically quite reasonable, boots to the desktop, and contains Risc OS 2. The battery damage was quite extensive but I believe I have repaired it all except for needing a new mouse port. So if anyone is interested in an A3000 project, PM me.