I assume that you have played with the jumpers, and that was not in play when it freak booted.
I'm thinking of the INT/EXT jumper for the CPU Clock source. It comes in play between 030 and 040/060 cpu cards.
I do not suspect the CIA chips since you have had it boot once and it was through making sure things are propperly seated and all contacts were clean. And like you say, the CIAs are soldered on.
So reconsider and find a new gut feeling. Which chips seemed to benefit most from your tlc.
Also, anything that can be taken out of the card should also be verified on a working motherboard.
Look over all caps also, are they dry or busted?
And finally, if the CIAs are busted. Look for two 22pin sockes, find your solder iron and find two new CIA agents and socket them :-)
Sounds like the card can be saved since you've had it alive once
