[aiharkness]

Check the quick settings and make sure notifications are not muted. If not.....

Let's step through it. And we'll deal with contact-specific ringtones separate from universal.

Pick an email account. Are you using a stock ringtone or a file you placed on the device. If the later, navigate to the file and make sure it will play. I'm assuming that either way there is no problem with the file. But if the file is corrupt and can't be played, that is a problem.

Go into settings to notifications. Set the notifications volume to high. Now go the screen to customize alerts for the selected email account. For now, set vibrate to on. Next, tap the tone field to drop down the selections and select one of the stock tones, and then select the previously selected ringtone. Each time you select a different tone the device should play it. Does that happen?

Now select the ringtone you want to use. Again, the tone should play. Tap the play icon at the bottom of the screen. Also, leave vibration enabled for now. Back your way out. Confirm save changes if prompted.

Now send yourself an email to that email address. You should, of course, hear the notification and the Z10 should vibrate. If not, what exactly happens?