My thought was that since the whine kicks in after about 30-60 sec and ramps up in pitch and level, then stops instantly when the woofer is shuts down (about 5 sec after hitting the switch, w a significant thump, that it might be a component failing in the woofer ampCould be, but during the initial seconds and minutes after turn-on, internal temperatures and consequently the operating parameters of all kinds of internal devices are changing significantly, which very conceivably could change circuit responses to externally induced noise or interference.
And I would guess that the turn-off thump is unrelated, and is just a consequence of some of the circuitry in the path through the woofer and the monitors de-energizing more quickly than the output stage of the amplifiers in the monitors. You might want to ask the previous owner if he had encountered the turn-off thump.
My instinct is that the odds are the problem is not a component failure, since it all apparently worked ok before it was shipped to you.
Good luck!
-- Al