Sounds like the capacitors to me.
Btw, capacitors leak electrolyte fluid with age. So just because the computer was never used/is in mint condition doesn't necessarily mean that the capacitors are good. In fact, a computer that has never been used is probably more prone to mechanical failure than a computer that was used more often as the components have never been sufficiently "exercised." It's like leaving a car in a garage for twenty years. Chances are it is not going to start, or function at all. I personally would recommend leaving the unit alone, considering it appears to be in mint condition, as you stated in the Trading Post forum. Just keep it as a show piece, and find another Classic II that has had more use, but has not been over abused.