It's a Yamaha P-105. Newly created projects are just fine - it only happens in projects created before I bought this keyboard.
I tried cutting and pasting into a new project, whose track was already set up for the proper output, though input was incorrect. Strange, when I first played back, no audio. Hitting one of the keyboard buttons this time, however, did not work. Then I changed the INPUT to Omni, and now it plays back fine.