I'd agree to first remove any CPU board and return the jumpers to use the onboard 68030. The CPU jumper configuration posted above looks as though it might be A3000D specific. The A3000T is a bit different, see what I have documented here under A3000T CPU JUMPERS:
http://amiga.serveftp.net/A3000_HardwareGuide/jumpers.htmlYou'll likely need to use the left hand column in the table.
Regarding your other post about damaged contents of the NVRAM causing the issue; the system will work fine (using defaults) if the NVRAM contents are lost, or even if the RP5C01 real time clock IC is removed. And invalid NVRAM is more likely to cause scsi.device to hang near the end of the ROM boot sequence, which isn't what you're seeing. The RP5C01 is socketed in the A3000T (the DIP18 package near the edge of the board, by the battery), so to eliminate the NVRAM theory you could remove the RP5C01 and see if that makes a difference.
Regarding the lack of floppy drive connection, that will cause some boot delay as the system tries to read a drive that isn't there, but it'll eventually get over it without indicating a system error.
And regarding capacitors, the system will typically boot without electrolytic capacitors fitted, let alone if the existing ones are reduced in capacity. That's a fairly wild stab in the dark.
Best guess it might have some kind of chip memory read/write issue, which since the minimalistic test in ROM only does a basic longword read/write every 16kB or something, and doesn't check for address issues, it will not indicate a green screen error for address faults. Instead the system will fail early on when it attempts to use the memory it tested to be good. Using DiagROM as suggested is helpful to see any obvious chip memory problems (but still won't detect address issues, which will also cause DiagROM to fail). I'd need to attach the hardware debugger to the board to see where it's failing during boot and exactly what's going on. It's not feasible to do this level of remote hardware fault finding using guesswork.
If you can't find anyone locally to repair the main board, I'm happy to take a look. The main board weighs around 2.6kg with packaging, shipping to NZ isn't the cheapest for that weight/volume, though I expect the board would likely be repairable.
http://amiga.serveftp.net