So the newly found piano does not run with batteries? If yes (there is a battery compartment and you put on fresh batteries), then the piano is probably working fine. If no, you need to dig deeper.
Did you try the 12V adapter with the 9V piano? Also note whether any lights come on when you plug in the adapter?
When you plug in the 9V adapter and connect to the machine, does the adapter gets warm to touch?
As you have found out, the adapter is fine but the machine may have some issues.