OK, the battery is off (the pins it was attached to still remain, or, at least, mostly), and the A500+, which was working perfectly before, seems to boot fine.
I'm not too sure about replacing the battery though... neither I or my father know much at all about electronics and soldering (I've only ever used an iron once, and that was years ago and only for a very brief period of time), and I've read that NiCd batteries are banned from sale in the EU for all but specialist purposes now. I read on one article that you can use a NiMH battery... is that true?