I am not so certain that your analog board is to blame. Given that leaky capacitors on the logic board cause all manner of misbehavio(u)r in Classics and their cousins, I would not jump to the conclusion that the analog board is the problem. Open it up and take a look around. In particular, look at the electrolytic caps that populate the board. If you see telltale smudges, then clean them off. A long-term fix, as JDW would certainly advocate, is to replace all of the electrolytics with fresh (tantalum) ones. But for troubleshooting purposes, a good clean often suffices.

If the caps collectively fail in the shorted condition, the power supply in the analog board could fail and release the magic smoke LCguy mentioned. But such an analog board failure would be a result, not a cause.