Thanks for your input! As for the battery, I have a big problem; as I said before, I'm positive this A4000 is a desktop machine put into a tower (the A4000T has Composite Video out, according to the Amiga Hardware sites). There is a ZorroIII expansion board and the WarpEngine attached to the motherboard; this means I can only see a small part of the motherboard. I can't locate the battery, and I'm pretty sure it's underneath the ZorroIII plane (it's huge).
I'm really not very inclined to disassemble the machine, at least without knowing it's working properly, since I'm affraid something would not work afterwards. It is a very old machine, and the last few years it was stored with the tower slightly open, wich means it's got plenty of dust inside.
I'll try to get the A520 as soon as possible to test it. I fear you might be right about putting power through the battery after all this time of inactivity!