@PulsatingQuasar:
First of all it sounds like you know what you're doing (see below about diagnosis). A good thing when starting with such complicated things.
Second thing: very strange that Ramsey was missing. Was it desoldered? (you mentioned soldering it). To me it's a sign that someone messed with the board before (they thought it was dead? knew it was dead?)
You mentioned replacing all the right stuff and the caps and also getting it to work at least once. VERY good sign.
Also your description about the "gray screen" (video signal present), Ctrl-A-A resets, white "flash" on power on, no ChipRAM=green scren, are "spot-on" for diagnosis. Good job. I'd agree with you that the CPU is working properly EVEN if you later describe the socket being bent and flexed (explain the flexed part again?).
Now, if it's not the socket, it's most likely one of the CIAs or some other part. I'd blame the CIA first, and the reason why is that it not only controls the stuff mentioned above, but if I recall correctly it's also the part that will map the Kickstart (I assume you've swapped the Kickstarts with known working ones, as well as all other socketed chips) which of course is necessary for the booting to occur. Therefore, if one (I don't remember which one controls the memory mapping, so you'll have to do some research on that and target that one first) of the CIAs is toast, the machine will power on, the CPU will be online, but no booting (aka. "almost black screen").
And now for the sweet part: hackery time: You don't have to remove the CIAs if you don't want to. What I did is take a PLCC socket which is the right size for the CIA, and flip it upside down, and "crown" the CIA. Then bend up the pins of the socket, and place the NEW CIA inside of the pins. Solder pins to CIA. Now you have a "complete crown". Last bit: cut the VCC pin on the old CIA (the one on the motherboard), so that there's a gap and therefore even side-ways pressure will not allow contact with the chip's portion of the pin. This will effectively disable the onboard CIA. Now place the "crown" on top of the CIA and boot. Note: you might have to file away some of the plastic of the PLCC socket so that the crown will sit and not pop-up. Hope these mini-instructions made sense. If I have some time I'll post photos.
Good luck mate and let us know how it goes.