@Tension.. LOL! I think he's a little more experienced with electronics than that
Wow, sounds like you're pretty handy with a logic probe! But did you try the simplest stuff first? Like removing and cleaning the pins where the 3640 interfaces the mobo? Horrible design IMO as they're too small. But since you're getting some kind of a picture... is it real dark with wavy lines? If so, recheck the video output. Do you have access to an RTG video card or just the AGA RGB output? How does it look when you hook it through the composite out? Alice might be bad if you've checked all the other components near her. If you don't want to go through the hassle of removing a SMD chip such as she, mobo's for the A4000 come up on ePay from time to time and not too expensive.
In any event and pardon my memory if this is not feasible, but I'd crazy glue a tiny heatsink (like from a PeeCee's video card) on her next time around...
Oh and Amigean stated what I overlooked... reseating ALL removable chips, or if they look corroded, cleaning their pins with light sandpaper or fiberglass brush (I guess they are no longer sold, but I have a large stash of replacements for mine). Only other bit of advice I could offer is to be sure your power supply caps are all good. GREAT idea to replace them anyway as they're known to go bad on any computer this age or older. Other components that fail in the power supply are bridge rectifiers and diodes - both of which can easily be tested with a DMM. Lastly, I'd check for cold solder joints everywhere (mobo and power supply especially), but especially where the power supply connector goes into the mobo.
