The postman never rings at all

I have a Mac mini with OS X 10.10.2. When mail arrives I get a banner but no sound, despite selecting one for new messages in Mail’s General preferences and having enabled ‘Play sounds for other mail actions’. In the Notifications preferences pane, Do Not Disturb is not checked, and ‘Play sound for notifications’ is turned on for Mail. I’ve added a rule that every message received should play a sound. Apple suggested that a PRAM reset would solve the problem but it hasn't Sound is set to maximum volume. Stephen Bishop You certainly seem to have done all the right things. The only thing I can add is to try changing the sound to ‘none’, clear ‘Play sounds for other mail actions’, and change them back again.

If that doesn’t help (and I’m not optimistic that it will), we are into the twilight zone. Assuming you hear sound in other apps, this is a bug in Mail. I’ve come across cases where iTunes was disabling the email notification sound, so there is some precedent here. But, unfortunately, no obvious fix.

Try starting up in Safe Mode (hold Shift from the moment you hear the startup sound) and open Mail. Does that make any difference?

If your Mac produces no sound, connect and disconnect something from the headphone jack a few times, and check the selected output in the Sound preferences pane.