A4000T appears to be dead

[metalman]

Are all SCSI devices unplugged? A locked SCSI bus will stop the boot process at a black screen

On a A3000 if the daughterboard is not seated it will stop the boot process at a black screen.

Does the power supply have 5 and 12vdc present?

[metalman]

Can you test individual parts on another machine identify working components?

Black screen = Power Supply, SCSI, CPU or Memory

Check that all chips are seated in the motherboard sockets.

[metalman]

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What I want to know is whether any chips can produce intermitent problems
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1) Memory
2) PIN & Chip Socketed Connections, pull and then reseat
3) Buster
4) SCSI chip (if devices connected)
5) Any chip above a certain temperature (would do it after its been running a while)

I think the machine would still boot even if the CIA's were dead

You might have a connection thats not making good contact,
pins, chip sockets, or card slot and you got a good connection the time it booted on the 030

The connections all oxidize with age, I suspect one is giving you the problems now.