One thing that I would certainly do with the Input Wire is to Tin it with Solder and cut so that no unisulated wire is protruding beyond the screws or Terminal Block. This may sound a little anal, but it is amazing how a proper installation can save problems later.It has been out of its box for many years. I mounted the board directly into the carriage at the time (I was reckless in my youth). There is nothing that looks fried. I can measure 24ac input. The speaker tests OK. That's about as far as my diagnostics have gone to this point.
Chip level repairs are not something I attempt unless stuck on a dessert island.....
As others have commented there seems to be no visible sign of damage, somewhat surprising if it emitted a fair volume of smoke.
This leads me to suspect that the speaker may be the problem.
Do you have access to a known good speaker of 8 ohms impedance and at least 2W output? If so it's worth a try before working on the board.
One thing that I would certainly do with the Input Wire is to Tin it with Solder and cut so that no unisulated wire is protruding beyond the screws or Terminal Block. This may sound a little anal, but it is amazing how a proper installation can save problems later.