I’ve been searching the net trying to figure out why I wasn’t getting audio of any kind on my laptop after installing Linux Mint. For future reference (and for anyone else who stumbles upon this) here’s what fixed it:

1. Open Volume Control (Double click on icon in menu bar)
2. Click ‘Preferences’
3. Check “External Amplifier”
4. Go to the newly visible “Switches” tab
5. Uncheck “External Amplifier” there.
6. Crank some music.