Thanks for your input. I've got an A520 modulator from eBay, and it's on it's way to me. That will do for now, to check if everything works. If it does work, then I'll investigate my Retina BLT Z3's outputs (still can't find manuals for the thing).
As for the battery, I'll really have to disassemble the Amiga, but it's not as bad as I thought. Only the Retina and the Micronik ZorroIII backplane have to come out to reach the battery. The mobo and the WarpEngine will stay in place. I'll probably take your kind offer, but let me find the time to take a better look at the A4000 (and probably post a few pictures).
Another related question: is it worth it to get the 3.1 ROMs? I'm guessing I have 3.0, because the mobo is a revision B. Having 3.1 ROMs would enable me to get OS3.9, right? Since I'm disassembling it, I could take care of that too.
I can't wait to see my Amiga working again, I feel like the first time I got it in Lisbon (from a 3D designer) and I had to wait the trip of more than 3 hours before I got home. I think I spent two whole weeks with it, installing things, setting up Workbench, playing The Settlers, Genetic Species demo, running Imagine, LightWave, ImageFX... it was incredible how Workbench/AmigaOS 3.1 was customizable, each one was different, I felt right at home. It was *my* Amiga, *my* Workbench.