It has the documented "FLUP FLUP FLUP" noise (the floppy drive sound) when it tries to power up. It's like it's in a constant loop of powering up and powering down and the FDD spinning up over and over, creating the flup noise, confirms this theory.

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This throws me a bit ... are you saying the FDD continually spins up and down? But if you remove the logic board, how can the sound continue if the FDD is no longer connected?

If you have the Pina book, then you have all the information available on the Flup assuming it's not multiple problems and you are diagnosing it correctly. I would do exactly as you are and go through each one step by step.