I'm a bit lazy and only skim read this thread, but unfortunately this doesn't sound like a typical capacitor problem, especially if you've seen no visual signs of leaking or deformation.
I've noted many of the common problems I've found with A3000 power supplies over the years here:
http://amiga.serveftp.net/A3000_HardwareGuide/booting-problems.htmlLook under the 'A3000 power supply common faults' section.
The standard repair process for any such switchmode supply: Check you have about 320V (150V for US models) across the main reservior capacitor - which is the big one. If not, it's a fuse or bridge rectifier fault. And usually these fail due to something else going wrong further into the supply. If yes, it's often a problem with the high voltage chopper transistors (though these usually fail short circuit which blows the fuse and sometimes damages the bridge rectifier in the process) or the low value series resistors (these always fail open circuit).
If that all checks out OK, you might have a switchmode controller fault which is more complicated to diagnose and repair, but this kind of fault is usually less likely.
Hope that helps, good luck with your repair job. And it certainly doesn't hurt to replace aging capacitors, so keep them on order.
