Recently I've also gotten no sound at all from playback when initiating a new music file and tapping notes in. I also checked the output sound in Audio setup and heard the hum just fine.  My headset was fully functional with any random youtube video in any browser, so it wasn't that the audio settings on the computer were faulty.

I came to realize that none the staffs in Finale had any instruments assigned to them, as if not assigning an instrument was the default setting for a new file.  I clicked on Windows--Score Manager--Instruments and then added a piano instrument to one of the staffs, which then filled in all of the instruments as piano, and voila, I had sound again during playback.  If piano isn't correct for any given staff line, just change that instrument to whatever is correct.

Hope this helps.

When I click on that, here is what I see.

Hmmm.  I had nothing for Device and Sound, but upon applying piano to Sound, I got playback.

Is SmartMusic for Device correct for your system?  I'm usually playing back through MIDI, a setting over in the menu in the middle of the screen (I'm not working in Finale currently).